{"as_of":"2026-08-09T23:38:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:d4b6b5af681ca00c66bb08ea1a509e6119dfe147c96bee46d41a86fe085bb0e3","coverage":[{"denominator":74,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":74,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-03T02:45:47.480682Z","state":"measured"},{"denominator":76,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":76,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-22T07:40:14.065515Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":1,"source":"arxiv_reference","source_observed_at":"2026-08-05T02:28:24.338817Z","state":"measured"}],"external_citation_measurements":[{"count":0,"observed_at":"2026-08-05T02:28:24.338817Z","source":"arxiv_reference"}],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"cited_work":{"arxiv_id":"2603.23969","doi":"10.48550/arxiv.2603.23969","metadata_source":"arxiv_reference","pith_arxiv_id":"2603.23969","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Matrix entries, unipotents, and linearity of amalgams","venue":"arXiv (Cornell University)","work_id":"e927af70-6fc6-409f-b684-5837a00f5b79","year":2026},"citing_paper":{"arxiv_id":"2605.21734","last_updated":"2026-05-20T20:48:53Z","snapshot_observed_at":"2026-08-02T05:30:22.574929Z","submitted_at":"2026-05-20T20:48:53Z","title":"Virtual specialness of the double","version":1},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-05-22T07:40:14.065515Z"},"links":{"cited_paper":"/paper/2603.23969","citing_paper":"/paper/2605.21734"},"observation_digest":"sha256:3936443314358b6e5640081101041bbfc566fc3f70a4e7d2a9b7968e9aa70fe7","observation_id":"26b16c1c-c055-4aa8-81e5-d882caf43023","resolution":{"observed_at":"2026-08-03T02:16:04.261606Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-05-22T19:24:20.499094+00:00","source":"crossref_status_cache"},{"observed_at":"2026-05-22T19:24:20.499094+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"cited_work":{"arxiv_id":"2603.23969","doi":"10.48550/arxiv.2603.23969","metadata_source":"arxiv_reference","pith_arxiv_id":"2603.23969","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Matrix entries, unipotents, and linearity of amalgams","venue":"arXiv (Cornell University)","work_id":"e927af70-6fc6-409f-b684-5837a00f5b79","year":2026},"citing_paper":{"arxiv_id":"2605.21734","last_updated":"2026-05-20T20:48:53Z","snapshot_observed_at":"2026-08-02T05:30:22.574929Z","submitted_at":"2026-05-20T20:48:53Z","title":"Virtual specialness of the double","version":1},"reference_index":42,"source":"arxiv_source","source_observed_at":"2026-05-22T07:40:14.065515Z"},"links":{"cited_paper":"/paper/2603.23969","citing_paper":"/paper/2605.21734"},"observation_digest":"sha256:1f0677957ef360d0bd83a93bcbfe5defc27cf9bdecb4966ee7c5618577d47516","observation_id":"9986f595-4e72-4008-bd1b-6fc297d016c8","resolution":{"observed_at":"2026-08-03T02:16:04.261606Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-05-22T19:24:20.499094+00:00","source":"crossref_status_cache"},{"observed_at":"2026-05-22T19:24:20.499094+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2603.23969/citation-record","integrity":"/paper/2603.23969/integrity","json":"/paper/2603.23969/citation-record.json","paper":"/paper/2603.23969"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"math/0405568","last_updated":"2004-05-29T02:35:53Z","snapshot_observed_at":"2026-07-07T05:41:19.906884Z","submitted_at":"2004-05-29T02:35:53Z","title":"Tameness of hyperbolic 3-manifolds","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"math/0405568","snapshot_observed_at":"2026-08-03T02:45:38.351531Z","title":"Agol , Tameness of hyperbolic 3-manifolds","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:38.351531Z"},"links":{"cited_paper":"/paper/math/0405568","citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:90af26a420d7a9b4438053f85d02393fe3aef63f66ad5c7ddf3f8500558410dc","observation_id":"1a124a00-c047-4e2c-bc68-b8f2ad3e7e1d","resolution":{"observed_at":"2026-08-03T02:45:38.351531Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"math/0612290","last_updated":"2006-12-11T22:49:31Z","snapshot_observed_at":"2026-07-07T06:02:51.661586Z","submitted_at":"2006-12-11T22:49:31Z","title":"Systoles of hyperbolic 4-manifolds","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"math/0612290","snapshot_observed_at":"2026-08-03T02:45:38.445220Z","title":"Preprint, arXiv :math/0612290 [math","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:38.445220Z"},"links":{"cited_paper":"/paper/math/0612290","citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:b5251fff0d4f2daf8bc6c925fa7c40c2382a5692fe1b2b892928eda5bbdd87db","observation_id":"4ad5e252-8c50-4e61-ae6d-262eef6eebcf","resolution":{"observed_at":"2026-08-03T02:45:38.445220Z","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":"2026-08-03T02:45:38.580754Z","title":"Math., 18 (2013), pp","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:38.580754Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:959b0f742b8535d81ef207fabd82a5b535a8b1c8cf8756d99d626f74a2e84133","observation_id":"8e169869-9501-4c0e-b561-83a059255b80","resolution":{"observed_at":"2026-08-03T02:45:38.580754Z","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":"2026-08-03T02:45:38.714724Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:38.714724Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:9821dd231f91ef68fcdd7a90c62735233954e3cabdc345efadfd8141724b5606","observation_id":"a0f3fe63-f27d-4b86-a127-158f7f21324a","resolution":{"observed_at":"2026-08-03T02:45:38.714724Z","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":"2026-08-03T02:45:38.879638Z","title":"Baker and D","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:38.879638Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:38473b973cbb3f3191c95d475bcb650700f961fa84aba4933a579d0be32bf3c2","observation_id":"29c9dc14-c2ae-465c-b0c7-716dcba16644","resolution":{"observed_at":"2026-08-03T02:45:38.879638Z","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":"2026-08-03T02:45:39.077879Z","title":"Baumslag , On the residual finiteness of generalized free products of nilpotent groups , Trans","venue":null,"work_id":null,"year":1963},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:39.077879Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:42c58d344d76429521f601138c6637d82bdc6b0804547c1a68dc9724c1170797","observation_id":"321837eb-0a6f-4c20-b6c6-648f4657b362","resolution":{"observed_at":"2026-08-03T02:45:39.077879Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2105.06897","last_updated":"2026-07-22T20:54:30Z","snapshot_observed_at":"2026-07-26T17:20:00.483716Z","submitted_at":"2021-05-14T15:32:37Z","title":"Subspace stabilisers in hyperbolic lattices","version":11},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2105.06897","snapshot_observed_at":"2026-08-03T02:45:39.220853Z","title":"Belolipetsky, N","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:39.220853Z"},"links":{"cited_paper":"/paper/2105.06897","citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:7d8067b60fda5c9b58f7ecd3033a6f3d3725b678ecc7a645a95cb33beaba0dd2","observation_id":"910fac4b-c698-48b5-99c3-35aac96e8b66","resolution":{"observed_at":"2026-08-03T02:45:39.220853Z","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":"2026-08-03T02:45:39.395533Z","title":null,"venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:39.395533Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:f50f6bf3681be3ffe0cddf9afcba41e5ce3e02775e43cb382dd259f10e3d04c7","observation_id":"e7d27339-b279-497b-a879-027a37781b44","resolution":{"observed_at":"2026-08-03T02:45:39.395533Z","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":"2026-08-03T02:45:39.536924Z","title":"Benoist , Five lectures on lattices in semisimple L ie groups , in G\\'eom\\'etries \\`a courbure n\\'egative ou nulle, groupes discrets et rigidit\\'es, vol","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:39.536924Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:851a18cb8c1d1f0318808afd186144f3cb0e125f2fdf0397d6f1d3b54fb6d71e","observation_id":"c2713e7a-1e4f-40d0-b57a-52dfbf6389b5","resolution":{"observed_at":"2026-08-03T02:45:39.536924Z","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":"2026-08-03T02:45:39.624845Z","title":"Berger , Les espaces sym \\'e triques non compacts , Ann","venue":null,"work_id":null,"year":1957},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:39.624845Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:58f82d689c752d6d500882e29f8b4d64a4bf6d65db21143aa3c4a1835bad0f92","observation_id":"6d25061e-9bf1-4a9d-b58a-398c8e0a4a3a","resolution":{"observed_at":"2026-08-03T02:45:39.624845Z","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":"2026-08-03T02:45:39.794828Z","title":"Bergeron , Premier nombre de B etti et spectre du laplacien de certaines vari\\'et\\'es hyperboliques , Enseign","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:39.794828Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:30f841812a77147076d52cb5eefcf8226d4d55dbb12aba1df72d55b8b94a56c4","observation_id":"033ed57f-b3af-431b-a343-09320105ea12","resolution":{"observed_at":"2026-08-03T02:45:39.794828Z","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":"2026-08-03T02:45:39.964877Z","title":"Bergeron, F","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:39.964877Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:2a8e8bf0d61ec2238ad607e4a4407a41d1b0f4070ca5caf3b965797076324e0f","observation_id":"e8aa6ade-f7e1-460b-9a69-356e047461ad","resolution":{"observed_at":"2026-08-03T02:45:39.964877Z","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":"2026-08-03T02:45:40.030592Z","title":"Bestvina and M","venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:40.030592Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:7434bbbd4309b73e762958395c12dceefc8814ca6db449560df99974c1abd898","observation_id":"9e6bdd4d-eaff-4fba-a3e0-75ec6bce0d4a","resolution":{"observed_at":"2026-08-03T02:45:40.030592Z","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":"2026-08-03T02:45:40.124768Z","title":"Bochi, R","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:40.124768Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:4c84efcdf7ac17eb25c2bd397c661b6fd4b1be306417672c15eeaae1f5d4eeb6","observation_id":"769f4532-fb97-4038-acf5-dc0cb8785169","resolution":{"observed_at":"2026-08-03T02:45:40.124768Z","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":"2026-08-03T02:45:40.210609Z","title":"Borel and Harish-Chandra , Arithmetic subgroups of algebraic groups , Ann","venue":null,"work_id":null,"year":1962},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:40.210609Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:99184a68b46a56fcdcc28c38158a4ce71d0e0b5716bc42c76566735ad88312c7","observation_id":"bf2c7ad3-0833-4b03-8ebd-0302bce7a089","resolution":{"observed_at":"2026-08-03T02:45:40.210609Z","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":"2026-08-03T02:45:40.364860Z","title":"Bourbaki , \\'El\\'ements de math\\'ematique","venue":null,"work_id":null,"year":1968},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:40.364860Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:0a06b6391a2fa724d24b00146b3ab5edc29a59e6c10a55547472e84ae6fd164a","observation_id":"9ec3e0e7-1d70-4273-81a9-bfa9eeeec62d","resolution":{"observed_at":"2026-08-03T02:45:40.364860Z","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":"2026-08-03T02:45:40.498917Z","title":null,"venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:40.498917Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:46f504448909104030fc49fdcf793eb05c1df64bf69317ff56f2d9ba93730ecc","observation_id":"74e82f5f-9e84-4699-b2dd-53225904453f","resolution":{"observed_at":"2026-08-03T02:45:40.498917Z","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":"2026-08-03T02:45:40.625837Z","title":null,"venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:40.625837Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:7b61e33bad9378af4e2682e8230985675b2407a8779673b722fd6d0d98b6e699","observation_id":"08d4a218-7228-4167-abcb-27cb4a61cd4c","resolution":{"observed_at":"2026-08-03T02:45:40.625837Z","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":"2026-08-03T02:45:40.767861Z","title":"Brooks , Circle packings and co-compact extensions of K leinian groups , Invent","venue":null,"work_id":null,"year":1986},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:40.767861Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:e940ad85e6d4dcbb2e4a9e6c7adfe51914d45c4d5ac287c11ed1150160f36e15","observation_id":"1f05f779-2856-416b-a715-074df0750166","resolution":{"observed_at":"2026-08-03T02:45:40.767861Z","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":"2026-08-03T02:45:40.945069Z","title":"Calegari and D","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:40.945069Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:31377905568719e35ef85d9f68ce5b19b00de69353e1f4bfc7d1d1ebd59ab063","observation_id":"94c1401b-47ed-4515-bb9d-92e8f2eef920","resolution":{"observed_at":"2026-08-03T02:45:40.945069Z","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":"2026-08-03T02:45:41.056607Z","title":null,"venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:41.056607Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:214f773bd1a86490f318483734a68ecd7392a6fac0a1675e5b01351c54aa6e95","observation_id":"d292ae7a-4ccb-475e-a5f3-3770f0022890","resolution":{"observed_at":"2026-08-03T02:45:41.056607Z","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":"2026-08-03T02:45:41.101307Z","title":"Preprint, arXiv :2510.21334 [math","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:41.101307Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:69db8d57f3dd476ee5babf88392c9a2b16b46689b976dde826e7cabba5d391e5","observation_id":"f6f82612-0789-4c2f-9bc6-e1853fd93c47","resolution":{"observed_at":"2026-08-03T02:45:41.101307Z","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":"2026-08-03T02:45:41.149432Z","title":"Chesebro, J","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:41.149432Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:7afb45575058450fcda7436ba48bf4cf6634485c065d06ef205a7405a9107268","observation_id":"2eff6cb6-0fd4-404b-b0dc-3278726241f0","resolution":{"observed_at":"2026-08-03T02:45:41.149432Z","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":"2026-08-03T02:45:41.226227Z","title":"Chevalley , Deux th\\'eor\\`emes d'arithm\\'etique , J","venue":null,"work_id":null,"year":1951},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:41.226227Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:ed2061f3a88d3fb797b4475f21e78ba611b81711841ec838b4320675a23a2ac2","observation_id":"ac3a4cc7-a1a4-41c0-bb13-73dfdf13f0d6","resolution":{"observed_at":"2026-08-03T02:45:41.226227Z","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":"2026-08-03T02:45:41.277974Z","title":"Chinburg and M","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:41.277974Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:e6da91109fd8d2a72810c8d856c2e3b514e18d6d0ac22b028c5024d80ac65d9c","observation_id":"4f29ade6-9a57-423d-a61a-7f1ac86d71f1","resolution":{"observed_at":"2026-08-03T02:45:41.277974Z","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":"2026-08-03T02:45:41.357242Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:41.357242Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:c1db5bc8e8130bd0e6721934732b7b3c1735a54b8c17316a39ed0389ef8de030","observation_id":"8ebe82b4-21b6-485d-bd4e-eb2844d8846e","resolution":{"observed_at":"2026-08-03T02:45:41.357242Z","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":"2026-08-03T02:45:41.478940Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:41.478940Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:f3897c325a810fa9af27ad17d607f8253ebda0c4c5f26a16202a08b444fa96c5","observation_id":"b22d0be3-9b44-48de-a65e-479209da3305","resolution":{"observed_at":"2026-08-03T02:45:41.478940Z","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":"2026-08-03T02:45:41.643880Z","title":"Corlette , Archimedean superrigidity and hyperbolic geometry , Ann","venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:41.643880Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:7f7f02194aac4c116ab4309428ed3530bfeecbe9858845e7a7c3da76e44adbea","observation_id":"374f1647-f5f3-4204-b889-ce070fa7609d","resolution":{"observed_at":"2026-08-03T02:45:41.643880Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2407.09439","last_updated":"2025-06-22T18:53:29Z","snapshot_observed_at":"2026-08-09T22:32:20.534766Z","submitted_at":"2024-07-12T17:20:16Z","title":"Combination theorems in convex projective geometry","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.09439","snapshot_observed_at":"2026-08-03T02:45:41.759173Z","title":"Danciger, F","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:41.759173Z"},"links":{"cited_paper":"/paper/2407.09439","citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:4105f42bdab5d8d3a765f3da32990f28d017338e1f9b70183363ee72f37bdb2d","observation_id":"6920907f-8bc5-4803-aa00-1dc92b4a6966","resolution":{"observed_at":"2026-08-03T02:45:41.759173Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2504.21802","last_updated":"2025-04-30T16:57:51Z","snapshot_observed_at":"2026-08-07T15:57:52.253461Z","submitted_at":"2025-04-30T16:57:51Z","title":"Anosov representations of amalgams","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2504.21802","snapshot_observed_at":"2026-08-03T02:45:41.892541Z","title":"Dey and K","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:41.892541Z"},"links":{"cited_paper":"/paper/2504.21802","citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:16319eb4b71ed51d601b862771b06b65c0efd05f171c801abdaaba3fd300eca1","observation_id":"98fc44fa-bf47-4333-975c-d26c8efe18a2","resolution":{"observed_at":"2026-08-03T02:45:41.892541Z","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":"2026-08-03T02:45:41.994814Z","title":"Drutu and M","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:41.994814Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:a274beec5748247a890e452a0a6f516c09c3322274d7c39d2201a081d3ab524d","observation_id":"ab5f65bb-ae44-4079-8634-19d6b8d6c6ea","resolution":{"observed_at":"2026-08-03T02:45:41.994814Z","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":"2026-08-03T02:45:42.124020Z","title":"Emery and I","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:42.124020Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:3c4b2945a3cd5dd43699296210a71e4f6304959797edb0e65cc25ce351ae1a2b","observation_id":"182a9109-1f99-4b0a-b342-e76a83bf2acb","resolution":{"observed_at":"2026-08-03T02:45:42.124020Z","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":"2026-08-03T02:45:42.247129Z","title":"Erschler , Not residually finite groups of intermediate growth, commensurability and non-geometricity , J","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:42.247129Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:59ecc665db4a5b1c3988f5cad97c1af284481f7ea62a489187b5ace01dd408aa","observation_id":"0b6bebf0-f1c2-46bd-9b26-34ec8ce027e6","resolution":{"observed_at":"2026-08-03T02:45:42.247129Z","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":"2026-08-03T02:45:42.396546Z","title":null,"venue":null,"work_id":null,"year":1984},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:42.396546Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:418a41c127c7aa4ecdc8eaec476f98cabafdd46bec333f324aab053b0de725b2","observation_id":"e9be6196-28c3-4334-99fa-6c64ac048c38","resolution":{"observed_at":"2026-08-03T02:45:42.396546Z","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":"2026-08-03T02:45:42.543735Z","title":"Gromov and R","venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:42.543735Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:f359be57cd599f5bb8e2e05107167fe80154b1ac1782c50df79e7355d54196c2","observation_id":"0ae1c128-3685-44f0-adc1-41912267f9c1","resolution":{"observed_at":"2026-08-03T02:45:42.543735Z","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":"2026-08-03T02:45:42.699225Z","title":"Guichard and A","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:42.699225Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:4b5326be1c46aae2231d385d797a5761444350c57033c95ce3e267725c2efd58","observation_id":"e0c1657a-51c9-451e-b597-85772a81d278","resolution":{"observed_at":"2026-08-03T02:45:42.699225Z","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":"2026-08-03T02:45:42.811204Z","title":"Haglund and D","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:42.811204Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:2f6ddf9f45ca85d72145a9e1e36b1edd74a2d13ff8cf8cd2480337ec42a8fb85","observation_id":"b79acb12-70f2-49b1-86de-77d52ac7f94f","resolution":{"observed_at":"2026-08-03T02:45:42.811204Z","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":"2026-08-03T02:45:42.910591Z","title":null,"venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:42.910591Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:45c1abb0b6330d50ee439f0118812af71fd9298d70951aa508c5db22b7f18493","observation_id":"d6b0b4a4-0e0d-429b-abbe-ebaa9dcaa34b","resolution":{"observed_at":"2026-08-03T02:45:42.910591Z","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":"2026-08-03T02:45:43.048779Z","title":null,"venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":39,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:43.048779Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:24acdcffa0ee9d3270b1077773c148f259b08dc8d3ae8cc7a6c6be55fcbbb7e9","observation_id":"4a9e3bea-637d-4844-8b6e-3cef1d5f6d6c","resolution":{"observed_at":"2026-08-03T02:45:43.048779Z","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":"2026-08-03T02:45:43.195954Z","title":null,"venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":40,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:43.195954Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:44743e033a81f8c48a498dd82b26bc2fb726420c11d5a636f81af91913e39e8f","observation_id":"d3137007-4a52-4686-b0b1-06b69926a4e3","resolution":{"observed_at":"2026-08-03T02:45:43.195954Z","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":"2026-08-03T02:45:43.277630Z","title":"Jacobson , Lie algebras , Dover Publications, Inc., New York, 1979","venue":null,"work_id":null,"year":1979},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":41,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:43.277630Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:5586777582920d270de06e305001101cd263d6bba19a83f9162a01167ff33ca1","observation_id":"e9e64737-069b-455f-bd24-d2ae0025354b","resolution":{"observed_at":"2026-08-03T02:45:43.277630Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2403.17964","last_updated":"2025-01-20T16:52:42Z","snapshot_observed_at":"2026-08-09T17:35:03.970154Z","submitted_at":"2024-03-14T18:47:11Z","title":"Quantifying separability in RAAGs via representations","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2403.17964","snapshot_observed_at":"2026-08-03T02:45:43.406402Z","title":"Kharlampovich and A","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":42,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:43.406402Z"},"links":{"cited_paper":"/paper/2403.17964","citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:69eaf3152376a1e1db15171485a85c26fb20be62a14dd7b648b0ea88ff668922","observation_id":"0b455ad0-3cec-4d71-8ecd-800c3d578651","resolution":{"observed_at":"2026-08-03T02:45:43.406402Z","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":"2026-08-03T02:45:43.510350Z","title":"Kneser , Normalteiler ganzzahliger S pingruppen , J","venue":null,"work_id":null,"year":1979},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":43,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:43.510350Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:2fecb0ce753c797f2e766383dfdbb485fd77ad8968af46ae2c48ed91dc1329dc","observation_id":"074370b7-bafb-4548-93e2-5c672e0dd773","resolution":{"observed_at":"2026-08-03T02:45:43.510350Z","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":"2026-08-03T02:45:43.588834Z","title":null,"venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":44,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:43.588834Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:2d88b8b79f779a8d1cd0b2231416e246d4ed189b54f57847f246733607d1f4a3","observation_id":"779eff19-7261-48f8-9b2e-aa4b0ce155d2","resolution":{"observed_at":"2026-08-03T02:45:43.588834Z","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":"2026-08-03T02:45:43.732791Z","title":null,"venue":null,"work_id":null,"year":1974},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":45,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:43.732791Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:e3c5860ea58d49f65e1830b96e1df91c942634797fb6dabf336021755b7614e1","observation_id":"5aafc8dd-6916-4d74-8d7b-8d14c445b378","resolution":{"observed_at":"2026-08-03T02:45:43.732791Z","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":"2026-08-03T02:45:43.882287Z","title":null,"venue":null,"work_id":null,"year":1979},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":46,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:43.882287Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:1078db85ab5ef92bbf3afd6f5f45ca19368ef5d9ee2a58775fc156b30c315624","observation_id":"357ed8b8-4218-40ba-8ef3-2dff8888bc2e","resolution":{"observed_at":"2026-08-03T02:45:43.882287Z","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":"2026-08-03T02:45:44.024833Z","title":null,"venue":null,"work_id":null,"year":1987},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":47,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:44.024833Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:77748472d3058c35a69f8c058667bfdddbb1f5fe51d4cc36ec28421e708e3382","observation_id":"0fdd6a8d-5b78-4913-a806-01ec69f5b20f","resolution":{"observed_at":"2026-08-03T02:45:44.024833Z","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":"2026-08-03T02:45:44.145829Z","title":"Louder, D","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":48,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:44.145829Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:58cebf2e1a16b822781a7b1209adf4363bd1aedc5257af0aa7b5babb9d6d4176","observation_id":"a3489a1c-af5f-4192-8d17-7b5ac773ba0f","resolution":{"observed_at":"2026-08-03T02:45:44.145829Z","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":"2026-08-03T02:45:44.293886Z","title":null,"venue":null,"work_id":null,"year":1956},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":49,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:44.293886Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:f17e6f07bb2f06e553aecc524e436c1a481f6c7c04361c1f24eb3305be2cebeb","observation_id":"c0efea43-22fc-427e-9d07-ac0a8d892a01","resolution":{"observed_at":"2026-08-03T02:45:44.293886Z","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":"2026-08-03T02:45:44.436352Z","title":null,"venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":50,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:44.436352Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:8b78b2ad714b9d7e1f1e2015fdfbaa09b8f2c51e2e6b2e6114de1eea0e66ec49","observation_id":"8370cbd2-4e30-4b5e-af97-81d0d72ad0de","resolution":{"observed_at":"2026-08-03T02:45:44.436352Z","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":"2026-08-03T02:45:44.556384Z","title":null,"venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":51,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:44.556384Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:0814898bb35554aaf14946050cf82da25c59596ae416ff490e7e5a8973e56bf9","observation_id":"52113df0-82f2-4ed6-8af8-0c814d81a855","resolution":{"observed_at":"2026-08-03T02:45:44.556384Z","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":"2026-08-03T02:45:44.694548Z","title":null,"venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":52,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:44.694548Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:28deb777af820b7e06e0f51874aac03999cf32a9a2553f2c806294b26e93b2e3","observation_id":"d029a588-2ad9-4117-9e6c-6c2e391cc8cb","resolution":{"observed_at":"2026-08-03T02:45:44.694548Z","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":"2026-08-03T02:45:44.853982Z","title":null,"venue":null,"work_id":null,"year":1976},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":53,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:44.853982Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:7035433918224ea1c9b9d4486a0f8e5aaf7998fbb047bcc112908dc7ef09f71d","observation_id":"a06ecd32-41b4-46ec-82ad-bbcf2645d637","resolution":{"observed_at":"2026-08-03T02:45:44.853982Z","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":"2026-08-03T02:45:44.997419Z","title":"Minasyan , Virtual retraction properties in groups , Int","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":54,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:44.997419Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:bc5e186c18c344f78824c052d71910d457648f57f6fdf9beef54f6c23da9ae90","observation_id":"2ab82e35-32c3-41a6-bbf3-96cab3e5a9c9","resolution":{"observed_at":"2026-08-03T02:45:44.997419Z","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":"2026-08-03T02:45:45.127306Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":55,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:45.127306Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:4097ee27798f3ba792941d95dc2de276d0471f704faaa05178028163228c1d68","observation_id":"118636a4-e7f1-4eed-a680-7385aa3db105","resolution":{"observed_at":"2026-08-03T02:45:45.127306Z","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":"2026-08-03T02:45:45.213360Z","title":null,"venue":null,"work_id":null,"year":1962},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":56,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:45.213360Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:b056c03fae1ca8098a2cfe0e16bf11463cb36495951e0bc8b03a074b49c93698","observation_id":"c5b86da4-876b-48f6-b6ba-18371a0b858e","resolution":{"observed_at":"2026-08-03T02:45:45.213360Z","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":"2026-08-03T02:45:45.319543Z","title":"Namazi and J","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":57,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:45.319543Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:5718a16885d3ffaa91b84ac34fc0672f8bfdfd66775cda87c9e8641847dd4622","observation_id":"b0ab9daf-ae5a-45a1-afdc-d6fe0e2e3072","resolution":{"observed_at":"2026-08-03T02:45:45.319543Z","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":"2026-08-03T02:45:45.475941Z","title":"Nisnevich , On groups isomorphically representable by matrices over a commutative field , Mat","venue":null,"work_id":null,"year":1940},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":58,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:45.475941Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:9ea1dc57ed9180cc17238c1a019d5a9e02e542b338cc1d12d1077cb6b9ff70a9","observation_id":"e6c46f9f-ee31-450f-aa92-dd9d7c0567a2","resolution":{"observed_at":"2026-08-03T02:45:45.475941Z","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":"2026-08-03T02:45:45.643154Z","title":"Ohshika , Realising end invariants by limits of minimally parabolic, geometrically finite groups , Geom","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":59,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:45.643154Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:fd55f359a57a8894c3d05a138b03e190580615610bd2802b0171150fea61d887","observation_id":"56fbca42-b5e2-43a7-859b-85a6a46ab8fc","resolution":{"observed_at":"2026-08-03T02:45:45.643154Z","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":"2026-08-03T02:45:45.783729Z","title":"Onishchik and E","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":60,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:45.783729Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:2254e06395d743f38ce74fb37bb03f087acc56217959f03745c76c58cbe36bee","observation_id":"20aecdd5-dbb7-41e8-8dec-b86e109496da","resolution":{"observed_at":"2026-08-03T02:45:45.783729Z","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":"2026-08-03T02:45:45.888211Z","title":"Parkkonen and F","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":61,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:45.888211Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:8cc214ee7c6c2e438f3cb49cb61701dfec107ad5b0da19936c74acf3f33fd422","observation_id":"28c85b97-879e-41ac-9ed8-3abebcf82377","resolution":{"observed_at":"2026-08-03T02:45:45.888211Z","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":"2026-08-03T02:45:45.990938Z","title":null,"venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":62,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:45.990938Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:2c1aaefdf9373112fd1ebcca1e0271d5bcdb15e52f90a3986508a19204dace8c","observation_id":"5cf85900-fc3e-40d3-be07-8c0dd5a1db5b","resolution":{"observed_at":"2026-08-03T02:45:45.990938Z","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":"2026-08-03T02:45:46.133739Z","title":"Potyagailo and E","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":63,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:46.133739Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:07fbb7f8b80a3c2f679528977d89bc4709bbbb015a13e68e55aa8a9a45f44cfc","observation_id":"08a859ca-7273-4cd0-9ffe-c4b9180b84d2","resolution":{"observed_at":"2026-08-03T02:45:46.133739Z","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":"2026-08-03T02:45:46.258940Z","title":"Prasad and M","venue":null,"work_id":null,"year":1972},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":64,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:46.258940Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:dbad7f13c5bded125c20ed99714e3fe28e73fa7d1615e7d61d739093b0a12a87","observation_id":"c0962781-d092-48f7-935b-b2f37d481258","resolution":{"observed_at":"2026-08-03T02:45:46.258940Z","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":"2026-08-03T02:45:46.370631Z","title":"Prasad and A","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":65,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:46.370631Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:2d55afffbbd519d9e5214cf18bfb32ce15886e0e9af5d5cf00a602e506394d5f","observation_id":"c5e826ad-87d2-4948-805e-2dbcca75ee6a","resolution":{"observed_at":"2026-08-03T02:45:46.370631Z","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":"2026-08-03T02:45:46.451811Z","title":null,"venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":66,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:46.451811Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:6679daecdb613da2e0710561c04acee4c27937ccdccac86e9a9f777f08f45c7f","observation_id":"d664d395-66e8-4292-8b23-ffe7821952e7","resolution":{"observed_at":"2026-08-03T02:45:46.451811Z","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":"2026-08-03T02:45:46.609670Z","title":"Serre , Trees , Springer-Verlag, Berlin-New York, 1980","venue":null,"work_id":null,"year":1980},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":67,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:46.609670Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:9680a4aec3e0cdb5decedd7669dc00402591d5dbc2b995f4dd071f0d9a610bb7","observation_id":"5f4492e3-9c20-43c6-ba71-b06989ca68b3","resolution":{"observed_at":"2026-08-03T02:45:46.609670Z","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":"2026-08-03T02:45:46.738969Z","title":null,"venue":null,"work_id":null,"year":1979},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":68,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:46.738969Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:c971cf92bcc806e6718c63b4c3bcb7c822ef6c75b81629cd9c721c0aa2df9c69","observation_id":"0997ddcd-a197-4946-ac62-219ca2b2af96","resolution":{"observed_at":"2026-08-03T02:45:46.738969Z","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":"2026-08-03T02:45:46.856335Z","title":"Tholozan and K","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":69,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:46.856335Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:5666b552af267f0b2a7af91920064e75e7c78bd00c76c234284204f943fe7ccc","observation_id":"41a4a379-44a8-42be-a5b2-4cd4baadaa90","resolution":{"observed_at":"2026-08-03T02:45:46.856335Z","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":"2026-08-03T02:45:46.984407Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":70,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:46.984407Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:97e09e3de1767c0fa1f77abea573c7d88f0bd7013c4df7cbe884ecdd198004c2","observation_id":"4cad7f06-cc12-41eb-a2a2-2e72ca3bb9ea","resolution":{"observed_at":"2026-08-03T02:45:46.984407Z","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":"2026-08-03T02:45:47.113055Z","title":"Tits , Free subgroups in linear groups , J","venue":null,"work_id":null,"year":1972},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":71,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:47.113055Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:7ac3d248feff5a5aebbba11ee840cb7a69f75b01cdf2f45d3d241c62d38a81ec","observation_id":"1a642f29-d2ea-40fb-a9ca-9c64e8ad5371","resolution":{"observed_at":"2026-08-03T02:45:47.113055Z","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":"2026-08-03T02:45:47.217530Z","title":null,"venue":null,"work_id":null,"year":1971},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":72,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:47.217530Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:25bd274fb5ff7d6b9686b938faf38731568389748fbe4a8d3df7b2dbaf36d58f","observation_id":"80e4d7cd-5b35-4519-832b-4f193d6e5f87","resolution":{"observed_at":"2026-08-03T02:45:47.217530Z","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":"2026-08-03T02:45:47.308454Z","title":null,"venue":null,"work_id":null,"year":1973},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":73,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:47.308454Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:293f9cce2cb95a748e1aa24ddb7b9bc9fc36c2fc624b68ad8986427409762622","observation_id":"9739f104-9ff6-4baf-9a79-e9f1ad36dea1","resolution":{"observed_at":"2026-08-03T02:45:47.308454Z","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":"2026-08-03T02:45:47.480682Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams","version":2},"reference_index":74,"source":"arxiv_source","source_observed_at":"2026-08-03T02:45:47.480682Z"},"links":{"citing_paper":"/paper/2603.23969"},"observation_digest":"sha256:6a41e2b1384010ada518dd24270d6fd88ef18a4741e64baf1ed887a8a04431fb","observation_id":"17e251e7-ecb6-4c2f-bf3c-ba1fe5fe2ffe","resolution":{"observed_at":"2026-08-03T02:45:47.480682Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2603.23969","last_updated":"2026-07-31T10:27:13Z","latest_version":2,"primary_category":"math.GR","snapshot_observed_at":"2026-08-09T15:24:21.361933Z","submitted_at":"2026-03-25T06:03:58Z","title":"Matrix entries, unipotents, and linearity of amalgams"},"reference_resolution":{"displayed":74,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":74,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":74},"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":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"thesis":"As of 9 August 2026, this Paper Citation Record lists 74 of 74 outbound references and 2 inbound Pith citation observations for arXiv:2603.23969."}