{"as_of":"2026-08-21T05:20:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:1ed7ad5706a2942086a9ed9c9a7c243e71851f3fc8c612b216f321a92ee4ca67","coverage":[{"denominator":54,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":54,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-08T13:59:06.846746Z","state":"measured"},{"denominator":54,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":54,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-20T06:33:59.587034+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/2502.07100/citation-record","integrity":"/paper/2502.07100/integrity","json":"/paper/2502.07100/citation-record.json","paper":"/paper/2502.07100"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T13:59:07.626018Z","title":"Abrams, Z","venue":null,"work_id":"85cc9468-0563-4294-b6af-66971484b4ed","year":2025},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.647485Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:6466eb61e703b2de063def35005b5b605c39ad9d19e654c0677112a7be50a1e7","observation_id":"a335f74c-1ca3-4c3b-bb5f-993fd98132fe","resolution":{"observed_at":"2026-08-08T13:59:07.629601Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-08T13:59:07.613080Z","title":"Afifurrahman, ‘Some counting questions for matrix products ’, Bull","venue":null,"work_id":"628cdda3-9548-4f49-9ff7-861436e2e540","year":2024},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.652319Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:ca6cd5afd500a26cd46e3469f6c9e958a4c4dbbffb6d65aa681a65c95cfa0bb8","observation_id":"88d632be-6932-4fca-908b-309c591bbbb9","resolution":{"observed_at":"2026-08-08T13:59:07.616820Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2407.08191","last_updated":"2025-02-12T05:32:41Z","snapshot_observed_at":"2026-08-17T18:57:44.260886Z","submitted_at":"2024-07-11T05:18:25Z","title":"A uniform formula on the number of integer matrices with given determinant and height","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.08191","snapshot_observed_at":"2026-08-08T13:59:06.656297Z","title":"Afifurrahman, ‘A uniform formula on the number of integer mat ri- ces with given determinant and height’, Preprint, 2024, available from https://arxiv.org/abs/2407.08191","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.656297Z"},"links":{"cited_paper":"/paper/2407.08191","citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:3a2069789304ac1d1057faa85f52c0db4e39f8eb407e43c8e1f146d6276b93f7","observation_id":"ed10cfb3-d15c-4f5e-bdbf-0b99bf78d9a5","resolution":{"observed_at":"2026-08-08T13:59:06.656297Z","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":"2026-08-08T13:59:07.602171Z","title":"Afifurrahman, V","venue":null,"work_id":"d7165436-6003-4dc7-9bee-40a4bdedc47a","year":null},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.661625Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:4b4dbbb7023539aa30b73047b82b557b6c9f21662e63f4632a56961284ffdce9","observation_id":"7a4e30aa-6ef7-428b-bf28-dc74a0f98861","resolution":{"observed_at":"2026-08-08T13:59:07.606029Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-08T13:59:07.591912Z","title":"Ahmadi and I","venue":null,"work_id":"389d761a-d446-417c-bb81-79e7fd7b4089","year":2007},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.665994Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:c22647681dd754e739414f247ac042f943ec2c87ff069da6df0c69687ef2cdfa","observation_id":"a057efe2-cabf-48a8-8701-73cdaafbaf55","resolution":{"observed_at":"2026-08-08T13:59:07.595373Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-08T13:59:07.580820Z","title":"Alon and J","venue":null,"work_id":"f360c82e-5ecb-481b-a5bb-4263303bbd94","year":2023},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.670149Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:c58c520a386b15d566e9388f88f9b52f8feee77ac9c29100769b091ddc2b99b3","observation_id":"dd886f76-b126-45b0-9e91-7f4dd7fb54a9","resolution":{"observed_at":"2026-08-08T13:59:07.584691Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-08T13:59:07.570749Z","title":"Amoroso, and E","venue":null,"work_id":"58a244f6-bd54-4d1a-84c1-9c7e5ca76980","year":2009},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.674020Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:498447a5b9d6253d5c55b89fe56c06dc8e130df47b0bc36eb00968de2ba83fa5","observation_id":"95ec1e78-9700-401c-a730-16fb9d7b12c6","resolution":{"observed_at":"2026-08-08T13:59:07.574349Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-08T13:59:07.560593Z","title":null,"venue":null,"work_id":"cc5b92f7-bc65-4d51-8aa1-c51b3404cad7","year":2021},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.678075Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:83f70828e1b6a7683b35471f9c0a0e568ded5cd63502cce8fc0b1d9dc408a509","observation_id":"06a2f357-ba04-4b79-9e3a-ac2e31d8dcef","resolution":{"observed_at":"2026-08-08T13:59:07.564215Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-08T13:59:07.550297Z","title":"Blomer and J","venue":null,"work_id":"7e991181-6b83-476a-8311-1920f1b05e2e","year":2023},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.681757Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:5925e2698b78573bcdedb7ec5a319642a3f8f865fadad97ca103adb97920dfca","observation_id":"8c511d7f-ca08-4fe5-a50f-53a2ce42c1b3","resolution":{"observed_at":"2026-08-08T13:59:07.553740Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-08T13:59:07.540273Z","title":"Blomer and C","venue":null,"work_id":"219b219e-ab65-4ca9-9ba3-6dc7b8c627e1","year":null},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.685479Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:6edfff44551c56c7bbc9d363816537e2e095e5559d535055932845eb209709a0","observation_id":"3ad0037d-47ee-4c97-9397-f3cfe8a8dbd7","resolution":{"observed_at":"2026-08-08T13:59:07.543857Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-08T13:59:07.530447Z","title":"Bourgain, M","venue":null,"work_id":"ea2b5a38-c523-4945-a704-c9a3735985b7","year":2014},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.689356Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:1fae1f652aa70ecddb1bab7967097e5b335584cb4d375e83e7c47a4ce940d603","observation_id":"3acbbf73-bf71-4008-9acd-cdd56848a589","resolution":{"observed_at":"2026-08-08T13:59:07.533873Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-08T13:59:07.519902Z","title":"Bourgain, V","venue":null,"work_id":"fd80ebcb-1ed3-403c-a4bb-26591babcad8","year":2010},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.693268Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:5883252e5910420aa85ecfbec07919258b07ebcb475b80be3309d3c871e6a6ac","observation_id":"33284dbb-4752-492a-bf28-b8618e4e1bb2","resolution":{"observed_at":"2026-08-08T13:59:07.523498Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-08T13:59:07.509788Z","title":null,"venue":null,"work_id":"b619c3f3-00eb-4ccc-94b6-4da9e0e7abd9","year":1987},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.697124Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:fb450b9ad6c88bf1b75e3700482502b71c093735d1e4344860d921523ef86ace","observation_id":"39387925-a69a-438f-94b3-e26ab0cb5ee2","resolution":{"observed_at":"2026-08-08T13:59:07.513181Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2409.01920","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T13:59:07.121839Z","title":"Browning, W","venue":null,"work_id":"61f21304-c876-43a0-8989-fb4c4c06eeb5","year":2024},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.701197Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:a9f2385f1342ac6902707d7d74387460a3a3e13a3bfecf07d826d98b00351930","observation_id":"4875f5a7-21af-4b78-9304-e4aca1011448","resolution":{"observed_at":"2026-08-08T13:59:07.127106Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-08T13:59:07.499658Z","title":"Bulinski, A","venue":null,"work_id":"44b41a5e-a1e6-4ada-b7f8-aed319d62410","year":null},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.704806Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:17350b30768e5e0b6c886c0802971a102f1eada4e89db11658335ab92268c3dd","observation_id":"b0551603-7ecf-4176-91de-2ca20911f7ec","resolution":{"observed_at":"2026-08-08T13:59:07.503444Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-08T13:59:07.489671Z","title":"Bulinski and I","venue":null,"work_id":"be72b966-4039-4dd0-ace7-edf552986b3e","year":2024},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.708666Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:1a111b2d5a452820e88001b1ccf68e7745699d434d858fee5c777384aceca2d0","observation_id":"f6c761eb-7de5-4f01-a099-8bd2cf7d8a0b","resolution":{"observed_at":"2026-08-08T13:59:07.493181Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-08T13:59:07.479163Z","title":"Campos, M","venue":null,"work_id":"3a8e7d19-255b-45d6-af90-d5b337050450","year":2025},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.712311Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:0bd6fea971b6ecd75f8e67275bd871e0a1178bd28706c1951ba67b06a91ca043","observation_id":"b94ff428-dcac-43b1-8d4e-ed49e7ec65b3","resolution":{"observed_at":"2026-08-08T13:59:07.482553Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-08T13:59:07.468690Z","title":null,"venue":null,"work_id":"2e552b06-5180-4ef8-93eb-596745ff094f","year":1993},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.715765Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:819a70e9965fbf72476c20693402afc758d01ec973368224ebe30a9c34296a08","observation_id":"7eb94177-d63d-4a0e-8d8c-6993e2232698","resolution":{"observed_at":"2026-08-08T13:59:07.472231Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-08T13:59:07.458162Z","title":"Eberhard, ‘The characteristic polynomial of a random matrix ’, Combina- torica, 42 (2022), 491–527","venue":null,"work_id":"3ff5624d-0691-4671-8c48-45dbfa9f284a","year":2022},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.719164Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:eb570185dfadd83ddffc193bd43b6b190336cbed42b9129e5beb6bee69d62a78","observation_id":"420c0e7b-1613-4ac1-9d97-0ca491192105","resolution":{"observed_at":"2026-08-08T13:59:07.461926Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2212.07408","last_updated":"2023-07-17T15:53:31Z","snapshot_observed_at":"2026-08-19T15:23:44.411924Z","submitted_at":"2022-12-14T18:46:21Z","title":"Effective equidistribution of primitive rational points on expanding horospheres","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2212.07408","snapshot_observed_at":"2026-08-08T13:59:06.722774Z","title":"El-Baz, M","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.722774Z"},"links":{"cited_paper":"/paper/2212.07408","citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:5ced000f35ca0eff6f5118a812cd91a830b07395db70a6d9afc6aeff1cbc20b8","observation_id":"beaa1660-f8d1-4652-9d05-e34ed44d4aba","resolution":{"observed_at":"2026-08-08T13:59:06.722774Z","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":"2026-08-08T13:59:07.447880Z","title":"Eskin and Y","venue":null,"work_id":"39f558eb-b558-4606-a313-aeac736b098d","year":1995},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.726754Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:68c0c97b35ac3d3b15c7525c1c55e72ab929e44915ae101d847dffb745ea3dcd","observation_id":"aee74765-9186-4253-bb38-f70cf48e2408","resolution":{"observed_at":"2026-08-08T13:59:07.451294Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-08T13:59:07.437582Z","title":"Eskin, S","venue":null,"work_id":"33fd5968-6de5-40b1-b0a5-3ce53996c6c6","year":1996},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.730464Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:88e306a941066af837e70a9d4105cb145a2b070fdcab6c79b226ca20a479b2d3","observation_id":"35b0490e-834d-453e-a390-b214e49eebab","resolution":{"observed_at":"2026-08-08T13:59:07.441123Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-08T13:59:07.427946Z","title":null,"venue":null,"work_id":"6e365f64-45f6-4822-a597-45d873634a99","year":2002},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.733908Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:05feb72a722684f32f3f49660784c38314297d241319feb9c67fc00fff8453e6","observation_id":"baeb8f99-4c0b-438d-9c2a-75ead013b1d0","resolution":{"observed_at":"2026-08-08T13:59:07.431317Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-08T13:59:07.417855Z","title":"Feit and N","venue":null,"work_id":"9108be01-34e9-402e-8a2e-48ca4208c825","year":1960},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.737367Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:5321a40438db64e7577765d6146e6521983add89925ebdde4f7aecd317725be9","observation_id":"144cacb9-dce5-4612-a403-844e5190e3aa","resolution":{"observed_at":"2026-08-08T13:59:07.421684Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-08T13:59:07.407964Z","title":"Ferber, K","venue":null,"work_id":"d1de9aa7-6d5c-4910-b0ed-40c69bd760dc","year":2021},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.740797Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:b34f5b44556fa97897383a844ddec61f60af4db9363f15532462c2942900a44d","observation_id":"41102f17-9455-47ec-9182-98fc07bf3743","resolution":{"observed_at":"2026-08-08T13:59:07.411415Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-08T13:59:07.396497Z","title":"Ferber, V","venue":null,"work_id":"7c777935-6fce-4d03-bc5d-4881e0e07f3e","year":2023},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.744669Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:8eff8d68a58fd4277cec164f79199703426656a4ec446a9d3b27cc4c34828a04","observation_id":"23f77fb8-9d26-44b6-95dd-d61ee5361247","resolution":{"observed_at":"2026-08-08T13:59:07.401234Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-08T13:59:07.385545Z","title":"Fulman, ‘Random matrices theory over finite fields’, Bull","venue":null,"work_id":"dea5f29a-4556-4641-acd2-b993010b86d6","year":null},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.747955Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:96878aa0695da5d0fed30fda9b0040f45d7da27439a4bb1c7de0b298603f7292","observation_id":"e2a007ef-8c78-4723-a70d-f04ca4296dd2","resolution":{"observed_at":"2026-08-08T13:59:07.389263Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-08T13:59:07.375439Z","title":"Fulman, and L","venue":null,"work_id":"deea53b6-e4d1-4036-819d-bfb0b5458151","year":2015},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.751806Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:8f126f6bd2d1b5ac165d6c05d8cf6bd77ad61ba39657f1073cf6045bc453b36f","observation_id":"14635930-056a-4900-a73a-609c5491a69d","resolution":{"observed_at":"2026-08-08T13:59:07.378905Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-08T13:59:07.364899Z","title":"Gerstenhaber, ‘On the number of nilpotent matrices with coe fficients in a finite field’, Illinois J","venue":null,"work_id":"b1b730ec-a50f-4aec-b757-6658c6f4e593","year":1961},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.755245Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:324f73f81670967caa547ef08e03363e790039b6678bd16d523614f3ea6705c8","observation_id":"9abcefa5-df79-4d31-93a4-3c6fdcce9ec1","resolution":{"observed_at":"2026-08-08T13:59:07.368551Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-08T13:59:07.354470Z","title":"Gorodnik, A","venue":null,"work_id":"e54fb0d2-93fc-46fd-94b6-25dc79094003","year":2017},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.759365Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:1b200b307fdc521bf01d33e78f9c59ba6453693a57b791c6ee957885807557e5","observation_id":"aacb44c2-dcae-432f-bac9-6682c29955c8","resolution":{"observed_at":"2026-08-08T13:59:07.357974Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2203.03880","last_updated":"2024-09-03T21:30:28Z","snapshot_observed_at":"2026-08-20T00:10:45.965928Z","submitted_at":"2022-03-08T06:56:26Z","title":"Integer matrices with a given characteristic polynomial and multiplicative dependence of matrices","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2203.03880","snapshot_observed_at":"2026-08-08T13:59:06.762704Z","title":"Habegger, A","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.762704Z"},"links":{"cited_paper":"/paper/2203.03880","citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:e17243bce011cf3e5e708ddec98cc203e666638f6da2338ae62927fc1a1603c3","observation_id":"a86d868e-3e19-44aa-91d5-3da609a3164f","resolution":{"observed_at":"2026-08-08T13:59:06.762704Z","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":"2026-08-08T13:59:07.344191Z","title":null,"venue":null,"work_id":"43a7d060-0069-45d1-af0d-b53101dd0879","year":2021},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.766613Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:1fbeca865a17dd03b2d93a75c5003aca65f4c344008c88ca8f69719ecfb9b33c","observation_id":"8d17f7a4-7d8e-48f5-9b0d-12caac649ff6","resolution":{"observed_at":"2026-08-08T13:59:07.347843Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-08T13:59:07.333825Z","title":null,"venue":null,"work_id":"1c534314-5036-4fe4-810e-724f51dfd8ac","year":1993},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.770004Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:1d3f773863d8a20f58ec2f60ddd5ac2ed777e1f391a224915a88788eba8adaf3","observation_id":"f72723b3-8e64-4b81-a8c4-7a8caaa7606e","resolution":{"observed_at":"2026-08-08T13:59:07.337505Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-08T13:59:07.323601Z","title":null,"venue":null,"work_id":"503bd487-ab19-4f4c-a42c-bd7919d01833","year":1994},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.773365Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:3677b4c24f25b652d8e0a1ef20e6a85e37b6ce3ae4b012dd792fcba9301db668","observation_id":"0ed2a7ef-55d7-4710-b2ad-a9f2ed9439ef","resolution":{"observed_at":"2026-08-08T13:59:07.327227Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-08T13:59:07.313265Z","title":null,"venue":null,"work_id":"8fd6ba4a-2987-493f-9f13-f91465a7a718","year":2019},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.776902Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:e3d664152ed735b65a6af5ab1982780dae60b1d32bb2b0ba8ec17545dc33d12b","observation_id":"ed37a11e-0699-41c3-9081-c54fe5445c0e","resolution":{"observed_at":"2026-08-08T13:59:07.316883Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-08T13:59:07.301882Z","title":"Koplewitz, ‘The corank of a rectangular random integer matr ix’,Lin","venue":null,"work_id":"20cf29bd-0d74-4cf9-aa58-c3d90b529c7a","year":2020},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.780696Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:5f93e851ffd67f174640a0aa1463f8944ee5bbf72724780e9ab2808c105a8b51","observation_id":"37d2422a-6d33-4421-87d9-92586de78c5a","resolution":{"observed_at":"2026-08-08T13:59:07.305665Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-08T13:59:07.291645Z","title":"Kwan and L","venue":null,"work_id":"d142090d-2859-4675-b9bd-57a11b4c9623","year":2022},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.784040Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:d8de3be969e424482c9462aab49f3b8c9d358573a1373b20e6d3b01d31c854a4","observation_id":"482d25c6-1568-4b5f-b59f-259939e95a42","resolution":{"observed_at":"2026-08-08T13:59:07.295275Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2310.09052","last_updated":"2025-02-17T11:11:45Z","snapshot_observed_at":"2026-08-19T23:13:38.702198Z","submitted_at":"2023-10-13T12:21:53Z","title":"Number of characteristic polynomials of matrices with bounded height","version":2},"cited_work":{"arxiv_id":"2310.09052","doi":null,"metadata_source":"pith","pith_arxiv_id":"2310.09052","snapshot_observed_at":"2026-08-08T13:59:07.025729Z","title":"Number of characteristic polynomials of matrices with bounded height","venue":"math.NT","work_id":"7dc31033-9cc6-461b-b7d4-c53c5ec8be69","year":2023},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.787602Z"},"links":{"cited_paper":"/paper/2310.09052","citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:fa2b08b2cf53dcfa7347d399deeb671ba7997d02a0ac96bfeb1bcc749d8d526e","observation_id":"280e46ca-829c-44ec-abdf-3500e02f77e9","resolution":{"observed_at":"2026-08-08T13:59:07.029864Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-08T13:59:07.281502Z","title":"Mohammadi, A","venue":null,"work_id":"2dd32b7f-69ca-4977-841d-81e6ad63b10a","year":2024},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.791676Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:a0efe0410097c31f6bea2acd2baaf8dfba670568ed9ec5e7203a1e23b128b2bf","observation_id":"21245764-939e-4b5b-ae0a-eb3be7058396","resolution":{"observed_at":"2026-08-08T13:59:07.284827Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2411.10404","last_updated":"2025-03-20T11:27:00Z","snapshot_observed_at":"2026-08-17T14:14:04.766375Z","submitted_at":"2024-11-15T18:19:49Z","title":"On commuting pairs in arbitrary sets of 2x2 matrices","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2411.10404","snapshot_observed_at":"2026-08-08T13:59:06.795258Z","title":"Mudgal, ‘On commuting pairs in arbitrary sets of 2 ˆ 2 matrices’, Preprint, 2024, available from https://arxiv.org/abs/2411.10404","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.795258Z"},"links":{"cited_paper":"/paper/2411.10404","citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:16ee585a5874691cc3e8e89d6835c2971c38ae1257edd56319444afbe22ec87b","observation_id":"e508233b-e71b-44dd-b287-7866de6a5769","resolution":{"observed_at":"2026-08-08T13:59:06.795258Z","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":"2026-08-08T13:59:07.271469Z","title":null,"venue":null,"work_id":"0f195ab5-865d-49b2-ad23-44c6e407abc2","year":2020},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.799261Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:e36776be796e2d70aef7a3887ab5b183f4e2ae5a255f8508e1460248a4c5184c","observation_id":"9373d9e3-64ac-4ae3-886d-44a6b5b6eb6b","resolution":{"observed_at":"2026-08-08T13:59:07.274970Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-08T13:59:07.261037Z","title":null,"venue":null,"work_id":"529dca36-7cae-4e64-b7c0-e9521ca94755","year":2022},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.802861Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:c2af9a30a14e11d34a2ed8d5ba48204db6d2051be2ea5e17b9e75af2c8ca6187","observation_id":"11c9df4a-026d-4243-b566-4326a00c9bdd","resolution":{"observed_at":"2026-08-08T13:59:07.264701Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-08T13:59:06.806376Z","title":"Ostafe and I","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.806376Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:db10cd42b269529e17bd6d81f524514d82e8442c2e2cdc5662de4f0640a30009","observation_id":"238834ea-e0a9-4603-8103-c3c3338fd13c","resolution":{"observed_at":"2026-08-08T13:59:06.806376Z","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":"2026-08-08T13:59:07.249427Z","title":"Reiner, ‘On the number of matrices with given characteristic p olynomial’, Illinois J","venue":null,"work_id":"07a5c09a-70a4-4f3e-a10a-ea62488d3a38","year":1961},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.810154Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:175bf9bc86bb05b972d5a196015d6cac8aa744ecf3729c37606c88e2ca880f32","observation_id":"9505db65-02fb-467a-8129-2596d43410ba","resolution":{"observed_at":"2026-08-08T13:59:07.253665Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-08T13:59:07.237561Z","title":"Sanna, ‘On the distribution of the entries of a fixed-rank ran dom matrix over a finite field’, Finite Fields Appl","venue":null,"work_id":"4cbee966-2ae1-410d-abcc-dfdd9e1c1658","year":2024},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.813720Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:3c775a6242d5a14cb889f1d853ec40ebf37777ba6c6503efb61c10433a0edc2f","observation_id":"6b846758-4451-4c5f-9234-11d5141f3203","resolution":{"observed_at":"2026-08-08T13:59:07.241653Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-08T13:59:07.226241Z","title":"Schmidt, ‘The subspace theorem in diophantine approximation s,” Compos","venue":null,"work_id":"740689b7-5153-4062-b0f8-a3efdb770b34","year":1989},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.817289Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:bbc9b0fe408a7f6fc681ec4f10e0e17eec466bbaad895f8b44bb5cf837785bc3","observation_id":"bb11e2ff-a0fa-4082-9115-b46084f7e4c9","resolution":{"observed_at":"2026-08-08T13:59:07.230310Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-08T13:59:07.215159Z","title":"Shah, ‘Counting integral matrices with a given characteristic polynomial’, Sankhya: The Indian J","venue":null,"work_id":"6890dbd7-b6e8-4cbb-a6ff-8c47a682e147","year":2000},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.821000Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:f555ed9030c082902963d600725fd47cb5f70be925eba535365459bf849e7a9b","observation_id":"7d06be15-381d-46c4-8d2f-77e61e6e3262","resolution":{"observed_at":"2026-08-08T13:59:07.219074Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-08T13:59:07.203966Z","title":"Shapira and C","venue":null,"work_id":"e05587ea-c0dd-4e81-bf2d-d4e2e77b57ac","year":2019},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.825085Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:459abbed09d203d12d746fbeca1baa688650ca4f62615a4c11ef4a160c4300c5","observation_id":"58dd9823-7f79-4321-8772-106bede5c26d","resolution":{"observed_at":"2026-08-08T13:59:07.207850Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2408.04350","last_updated":"2024-08-08T10:23:22Z","snapshot_observed_at":"2026-08-19T09:17:52.365600Z","submitted_at":"2024-08-08T10:23:22Z","title":"On the determinants of matrices with elements from arbitrary sets","version":1},"cited_work":{"arxiv_id":"2408.04350","doi":null,"metadata_source":"pith","pith_arxiv_id":"2408.04350","snapshot_observed_at":"2026-08-08T13:59:06.877368Z","title":"On the determinants of matrices with elements from arbitrary sets","venue":"math.NT","work_id":"f7056e85-5ca8-4b48-b6c6-d52d7877d931","year":2024},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.828723Z"},"links":{"cited_paper":"/paper/2408.04350","citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:c60a57cae68699641c1228ee1980b52794a685d2dcf3ee5a46cf3589b2612201","observation_id":"c31adddf-6749-45a2-84d1-2c2a3e91d143","resolution":{"observed_at":"2026-08-08T13:59:06.883475Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-08T13:59:07.192216Z","title":null,"venue":null,"work_id":"663a0d94-2aa8-486c-bed3-0de09870d22c","year":2010},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.832391Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:81047d3d7a197387105e1c5b6be26a078a53db9c7a25882ba29bc2256625a087","observation_id":"ee479e20-6b94-4e17-b7f9-d1d1e89ad2b8","resolution":{"observed_at":"2026-08-08T13:59:07.195897Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-08T13:59:07.180587Z","title":"Tao and V","venue":null,"work_id":"f1a470a5-097c-44d6-8e1d-72a8c507608f","year":2009},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.836078Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:e31739d370620fe033c95153651b63bf1d5a542bcabd4235214cbd15a7728d80","observation_id":"7a222c58-e804-4346-92a8-656bb24d7ea3","resolution":{"observed_at":"2026-08-08T13:59:07.184250Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-08T13:59:07.169617Z","title":"Vu, ‘Recent progress in combinatorial random matrix theory ’, Probability Surveys, 18 (2021), 179–200","venue":null,"work_id":"63f2d28a-fe4e-4d6c-b2ac-8a0047644b0d","year":2021},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.839844Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:d4d64654b08114d5128a4445b8cbd99a1db68da52f9394b7a267c1c2d9b9904e","observation_id":"933599b0-26d0-4b46-8c80-106547649eb6","resolution":{"observed_at":"2026-08-08T13:59:07.173294Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-08T13:59:07.158364Z","title":"Wei and F","venue":null,"work_id":"2f215e1a-5994-4c11-acce-062d1b751be5","year":2016},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.843341Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:5da5139336363a848a72c27040bf766ab51450d8084df5354fb9ca20378771b9","observation_id":"1dd15604-f1cc-43a7-96b1-41d9763fbc10","resolution":{"observed_at":"2026-08-08T13:59:07.162245Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-08T13:59:07.147014Z","title":"cn´2 “ 0, A´µpnq, c n´1 “ 0 and cn´2 ‰ 0, A´νpnq, c n´1 ‰ 0, where βpnq is given by ( B.1) and furthermore λpnq “ $ ’ ’ ’ ’ ’ & ’ ’ ’ ’ ’ % 1{2, n “ 5, 1, n","venue":null,"work_id":"be7bc2f7-7acc-4f83-bf5f-0db33f78df58","year":2019},"citing_paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-08T13:59:06.846746Z"},"links":{"citing_paper":"/paper/2502.07100"},"observation_digest":"sha256:8a25833d2a0bded2807afd8ac8a26ae2d703b5723ea6a5789378dfe050710bb7","observation_id":"db510976-3471-46ca-af17-d3fb5251db36","resolution":{"observed_at":"2026-08-08T13:59:07.150798Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2502.07100","last_updated":"2025-02-10T22:45:33Z","latest_version":1,"primary_category":"math.NT","snapshot_observed_at":"2026-08-18T20:14:33.117872Z","submitted_at":"2025-02-10T22:45:33Z","title":"Counting matrices over finite rank multiplicative groups"},"reference_resolution":{"displayed":54,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":16,"verified_exact":3,"verified_fuzzy":35},"total_outbound_references":54},"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":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"thesis":"As of 21 August 2026, this Paper Citation Record lists 54 of 54 outbound references and 0 inbound Pith citation observations for arXiv:2502.07100."}