{"as_of":"2026-08-17T22:56:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:4e80133001e3b6f34f73d88f778a4592e792d7af5128b4c01363782954e2f8f0","coverage":[{"denominator":22,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":22,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-16T11:31:17.387378Z","state":"measured"},{"denominator":23,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":23,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-17T06:30:58.91139+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-14T11:15:04.329014Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2504.15510","last_updated":"2026-06-10T01:33:24Z","snapshot_observed_at":"2026-08-16T11:22:34.392765Z","submitted_at":"2025-04-22T01:10:31Z","title":"Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2504.15510","snapshot_observed_at":"2026-07-14T11:15:04.329014Z","title":"arXiv preprint arXiv:2504.15510 , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.10500","last_updated":"2026-07-11T22:45:00Z","snapshot_observed_at":"2026-08-15T04:26:03.425135Z","submitted_at":"2026-07-11T22:45:00Z","title":"Adaptable Regularized CCA Tests for Independence of High-Dimensional Random Vectors","version":1},"reference_index":144,"source":"arxiv_source","source_observed_at":"2026-07-14T11:15:04.329014Z"},"links":{"cited_paper":"/paper/2504.15510","citing_paper":"/paper/2607.10500"},"observation_digest":"sha256:881a143334ea4e1c062d4e837f2c23e5c9658e005f90290642d36b1389b843ad","observation_id":"c57e03ce-7d57-4395-83f2-86116cc2d6e1","resolution":{"observed_at":"2026-07-14T11:15:04.329014Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2504.15510/citation-record","integrity":"/paper/2504.15510/integrity","json":"/paper/2504.15510/citation-record.json","paper":"/paper/2504.15510"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:31:17.738642Z","title":"Isotropic local laws for sample covariance and generalized Wigner matrices","venue":null,"work_id":"71719e3b-a767-49f5-85b8-ab0339efcb9f","year":2014},"citing_paper":{"arxiv_id":"2504.15510","last_updated":"2026-06-10T01:33:24Z","snapshot_observed_at":"2026-08-16T11:22:34.392765Z","submitted_at":"2025-04-22T01:10:31Z","title":"Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses","version":3},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-16T11:31:17.291417Z"},"links":{"citing_paper":"/paper/2504.15510"},"observation_digest":"sha256:c7d94399e23d3f0885ec2ed7da6a1c9e6db27368e9586345ab592f1ae57b05f0","observation_id":"b8accb99-515a-45a0-86e7-b80be7999ae5","resolution":{"observed_at":"2026-08-16T11:31:17.743365Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1410.2848","last_updated":"2014-10-10T17:45:18Z","snapshot_observed_at":"2026-08-14T23:16:11.068149Z","submitted_at":"2014-10-10T17:45:18Z","title":"Two-Sample Tests for High Dimensional Means with Thresholding and Data Transformation","version":1},"cited_work":{"arxiv_id":"1410.2848","doi":null,"metadata_source":"pith","pith_arxiv_id":"1410.2848","snapshot_observed_at":"2026-08-16T11:31:17.439559Z","title":"Two-Sample Tests for High Dimensional Means with Thresholding and Data Transformation","venue":"stat.ME","work_id":"f76d2bb7-2d07-45ee-8969-6f0533bb0e02","year":2014},"citing_paper":{"arxiv_id":"2504.15510","last_updated":"2026-06-10T01:33:24Z","snapshot_observed_at":"2026-08-16T11:22:34.392765Z","submitted_at":"2025-04-22T01:10:31Z","title":"Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses","version":3},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-16T11:31:17.296586Z"},"links":{"cited_paper":"/paper/1410.2848","citing_paper":"/paper/2504.15510"},"observation_digest":"sha256:735c0d245b613498d9c85b7e76702d65ed211db5b13365f7296c24ddb92c381a","observation_id":"7ffa41f6-6bd6-4fd1-acb2-cf9f83dcbc83","resolution":{"observed_at":"2026-08-16T11:31:17.446444Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:31:17.695192Z","title":"(3) There exists sufficiently small constants C ą 0 and C1ą 0 such that for all zPtE` iη : |E´ Θ1|ď C, 0ăηăC´1u inf τPSGλ |τ`qpzq|ě C1, whereSGλ is the support of Gλ","venue":null,"work_id":"a7e5a944-e333-4c6a-b72f-c42d3f2eedd6","year":1995},"citing_paper":{"arxiv_id":"2504.15510","last_updated":"2026-06-10T01:33:24Z","snapshot_observed_at":"2026-08-16T11:22:34.392765Z","submitted_at":"2025-04-22T01:10:31Z","title":"Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses","version":3},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-16T11:31:17.316629Z"},"links":{"citing_paper":"/paper/2504.15510"},"observation_digest":"sha256:f083adcd074e82ee1ba0db2e10becf6a368f7072626ec2a963397fb1dd8ea6db","observation_id":"5f0fcd88-8bdb-4112-8162-6e5c9e7a528b","resolution":{"observed_at":"2026-08-16T11:31:17.699763Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:31:17.680858Z","title":"Let zPD and suppose that |˜z´z|ď δpzq, where ˜z“´ 1{upzq` γ2ϕp´upzqq","venue":null,"work_id":"dde473ed-f73b-40f6-82d7-969da0feae1f","year":2024},"citing_paper":{"arxiv_id":"2504.15510","last_updated":"2026-06-10T01:33:24Z","snapshot_observed_at":"2026-08-16T11:22:34.392765Z","submitted_at":"2025-04-22T01:10:31Z","title":"Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses","version":3},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-16T11:31:17.322010Z"},"links":{"citing_paper":"/paper/2504.15510"},"observation_digest":"sha256:529ece0c6e1300add40d6f7ba001cac0e4cf823710c3c60ffabebbf63c39d3f8","observation_id":"9f67c5a3-ae6a-42b8-838f-8d4cdde95644","resolution":{"observed_at":"2026-08-16T11:31:17.685543Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:31:17.665795Z","title":"Let zPQ and suppose that |˜z´z|ď δpzq, where ˜z“vpzq` „ 1`γ2 ż τdF Σ8pτq ´τvpzq` λ ȷ´1","venue":null,"work_id":"f675d6e5-d011-4b6f-bee0-4a9a438c0ff1","year":2017},"citing_paper":{"arxiv_id":"2504.15510","last_updated":"2026-06-10T01:33:24Z","snapshot_observed_at":"2026-08-16T11:22:34.392765Z","submitted_at":"2025-04-22T01:10:31Z","title":"Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses","version":3},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-16T11:31:17.326567Z"},"links":{"citing_paper":"/paper/2504.15510"},"observation_digest":"sha256:1ebaf1244e898e38665862b26468e4a0b010a69f002038e2e6a049d8c1c25375","observation_id":"8fe15588-6bbc-47e1-bb9d-c399e900830d","resolution":{"observed_at":"2026-08-16T11:31:17.670729Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:31:17.652129Z","title":"(ii) The averaged local law in Qppq holds as ˆϕppzq´ ϕppzq“ Oă ˆ 1 n2η ˙ , where ˆϕppzq“ p´1trRpzq","venue":null,"work_id":"07e58518-71a7-45d9-a2b1-8f7023f6558c","year":2017},"citing_paper":{"arxiv_id":"2504.15510","last_updated":"2026-06-10T01:33:24Z","snapshot_observed_at":"2026-08-16T11:22:34.392765Z","submitted_at":"2025-04-22T01:10:31Z","title":"Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses","version":3},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-16T11:31:17.331378Z"},"links":{"citing_paper":"/paper/2504.15510"},"observation_digest":"sha256:6b2f3b5fdf97f28877893ab384620823d9f5d509b7e854ef2f0a9e1f9d3de99e","observation_id":"e9ffe472-2516-417c-a29f-8996929807ea","resolution":{"observed_at":"2026-08-16T11:31:17.656219Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:31:17.639466Z","title":"We have }J}ď C η3, }BzJ}ď C η6","venue":null,"work_id":"5a514ca3-b0fe-474c-9779-331b26d5596b","year":2017},"citing_paper":{"arxiv_id":"2504.15510","last_updated":"2026-06-10T01:33:24Z","snapshot_observed_at":"2026-08-16T11:22:34.392765Z","submitted_at":"2025-04-22T01:10:31Z","title":"Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses","version":3},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-16T11:31:17.336185Z"},"links":{"citing_paper":"/paper/2504.15510"},"observation_digest":"sha256:259b08f8f70674e7833cdf86ccc9787fb39aa93f41a183e48d3374c5d0334008","observation_id":"2a69cd31-6ff5-4f46-853e-150bd689c340","resolution":{"observed_at":"2026-08-16T11:31:17.643356Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:31:17.626085Z","title":null,"venue":null,"work_id":"468da937-390c-43a2-8409-d724ca71044c","year":2014},"citing_paper":{"arxiv_id":"2504.15510","last_updated":"2026-06-10T01:33:24Z","snapshot_observed_at":"2026-08-16T11:22:34.392765Z","submitted_at":"2025-04-22T01:10:31Z","title":"Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses","version":3},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-16T11:31:17.340686Z"},"links":{"citing_paper":"/paper/2504.15510"},"observation_digest":"sha256:b31fd6b6efc699874b93873de4b35139c939e650e3b9daa74ef935bbcca2f357","observation_id":"ebd0f181-3941-457c-a9ba-d6219413812a","resolution":{"observed_at":"2026-08-16T11:31:17.630059Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:31:17.611572Z","title":"Let us first estimate Λ o","venue":null,"work_id":"15d2e387-ab30-43bb-a346-3dabc8fe8bf1","year":2014},"citing_paper":{"arxiv_id":"2504.15510","last_updated":"2026-06-10T01:33:24Z","snapshot_observed_at":"2026-08-16T11:22:34.392765Z","submitted_at":"2025-04-22T01:10:31Z","title":"Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses","version":3},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-16T11:31:17.344571Z"},"links":{"citing_paper":"/paper/2504.15510"},"observation_digest":"sha256:d6dfc9f1edd3eda22a09700a218a81c01c2880b440cba3945a2b4e7fac22c1bd","observation_id":"ebcb2337-7e4d-4aa5-b92e-fc4a6fac882f","resolution":{"observed_at":"2026-08-16T11:31:17.616120Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:31:17.596958Z","title":"Applying Lemma S.4.6 or Corollary S.4.3, when ηě 1, |ˆϕp´ϕp|ď Cp|δ1|`| δ2|q ă ΨB ăn´1{2 2","venue":null,"work_id":"19922812-6b9c-44c5-8817-e36ec7dca9d7","year":2014},"citing_paper":{"arxiv_id":"2504.15510","last_updated":"2026-06-10T01:33:24Z","snapshot_observed_at":"2026-08-16T11:22:34.392765Z","submitted_at":"2025-04-22T01:10:31Z","title":"Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses","version":3},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-16T11:31:17.348610Z"},"links":{"citing_paper":"/paper/2504.15510"},"observation_digest":"sha256:4d0e232867e98791760f34db6db01435e29d4fd763487c0834d570d84c16a7b6","observation_id":"b8f9fb46-9f96-4d89-adee-e2aef21b7f93","resolution":{"observed_at":"2026-08-16T11:31:17.601548Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:31:17.580664Z","title":"Then on QppqYQppq away we have 1 p pÿ u“1 1 pλ{σu´z´ 1 n2 řp`n2 i“p`1 Jiiq2p1´ Euq 1 Juu “Oă ` Υ2˘ and 1 n2 p`n2ÿ i“p`1 p1´ Eiq 1 Jii “Oă ` Υ2˘","venue":null,"work_id":"626adab2-9f5a-4108-9a30-c99b43569952","year":2017},"citing_paper":{"arxiv_id":"2504.15510","last_updated":"2026-06-10T01:33:24Z","snapshot_observed_at":"2026-08-16T11:22:34.392765Z","submitted_at":"2025-04-22T01:10:31Z","title":"Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses","version":3},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-16T11:31:17.352497Z"},"links":{"citing_paper":"/paper/2504.15510"},"observation_digest":"sha256:eb75f44ed45f1d83475744b0f9d66f6d29a7e33474200e96b67b753763e6b05e","observation_id":"4f600a91-8bb3-4b8e-9972-2529789cac6b","resolution":{"observed_at":"2026-08-16T11:31:17.586418Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:31:17.565166Z","title":"Therefore, to show ˇˇˇˇˇ 1 p pÿ j“1 fpℓjpGλqq´ ż fpτqdGλpτq ˇˇˇˇˇ ă 1 n2 , it suffices to show ¿ ˆR |fpzq| ˇˇˇˆϕppzq´ ϕppzq ˇˇˇdz ă 1 n2","venue":null,"work_id":"7f4f3b19-a81b-4f17-ae41-390eda272ea6","year":2017},"citing_paper":{"arxiv_id":"2504.15510","last_updated":"2026-06-10T01:33:24Z","snapshot_observed_at":"2026-08-16T11:22:34.392765Z","submitted_at":"2025-04-22T01:10:31Z","title":"Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses","version":3},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-16T11:31:17.356527Z"},"links":{"citing_paper":"/paper/2504.15510"},"observation_digest":"sha256:8bd1ca72ea714822ecf17a293bb064a2ccdee9a6eacc6e66b1e54fcdf0995b60","observation_id":"850edf40-f6e9-449a-9464-caa1e20c1017","resolution":{"observed_at":"2026-08-16T11:31:17.570119Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:31:17.550780Z","title":"local laws","venue":null,"work_id":"ebf36eed-3aa5-4879-b469-ec85fa770ca4","year":2012},"citing_paper":{"arxiv_id":"2504.15510","last_updated":"2026-06-10T01:33:24Z","snapshot_observed_at":"2026-08-16T11:22:34.392765Z","submitted_at":"2025-04-22T01:10:31Z","title":"Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses","version":3},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-16T11:31:17.360865Z"},"links":{"citing_paper":"/paper/2504.15510"},"observation_digest":"sha256:c9ed2771571bfba6e75f6aa07a3f964b0020cfff0d215dc04d05223748e3f748","observation_id":"1ef244ac-db55-4e06-9413-2cfd6ca01279","resolution":{"observed_at":"2026-08-16T11:31:17.555080Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:31:17.535385Z","title":"Let ˆΘp1“ ˆfp´ ˆβpq and ˆΦpzq“ d ℑˆqppzq n1η ` 1 n1η","venue":null,"work_id":"b63a87f3-35ce-4c49-9ce2-ed89c84273ae","year":2017},"citing_paper":{"arxiv_id":"2504.15510","last_updated":"2026-06-10T01:33:24Z","snapshot_observed_at":"2026-08-16T11:22:34.392765Z","submitted_at":"2025-04-22T01:10:31Z","title":"Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses","version":3},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-16T11:31:17.364887Z"},"links":{"citing_paper":"/paper/2504.15510"},"observation_digest":"sha256:da25df1b85757a15f9db75e5200f931446bc91539eabbcfa7825103c59fdd03c","observation_id":"ebf4bad1-79d4-4be6-8149-a3606d1a58b8","resolution":{"observed_at":"2026-08-16T11:31:17.540696Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:31:17.518991Z","title":"Therefore, ´ˆqppzq is away from the support of Gλ","venue":null,"work_id":"3f7548c3-816b-411a-9bc7-546467791f5e","year":2016},"citing_paper":{"arxiv_id":"2504.15510","last_updated":"2026-06-10T01:33:24Z","snapshot_observed_at":"2026-08-16T11:22:34.392765Z","submitted_at":"2025-04-22T01:10:31Z","title":"Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses","version":3},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-16T11:31:17.368971Z"},"links":{"citing_paper":"/paper/2504.15510"},"observation_digest":"sha256:3d702ac69387eaa15ee9fcd79bcf91e1b7b88adb0a0afbac2fe5fbd86a5f6b35","observation_id":"04257bee-d96f-4f8f-8644-8ffaaacd0b84","resolution":{"observed_at":"2026-08-16T11:31:17.524282Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:31:17.504234Z","title":null,"venue":null,"work_id":"49a3dd5b-a1bf-4986-bb5a-a5caed3870ac","year":2018},"citing_paper":{"arxiv_id":"2504.15510","last_updated":"2026-06-10T01:33:24Z","snapshot_observed_at":"2026-08-16T11:22:34.392765Z","submitted_at":"2025-04-22T01:10:31Z","title":"Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses","version":3},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-16T11:31:17.373609Z"},"links":{"citing_paper":"/paper/2504.15510"},"observation_digest":"sha256:1461254e275a1f037b48f15ad2be5a702240e2900ca70a0f52eefef76ccd9510","observation_id":"245fbb02-55b7-4710-8dde-03c0f388bb33","resolution":{"observed_at":"2026-08-16T11:31:17.508341Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:31:17.489102Z","title":"1 pνTD1{2pW2`λIpq´1D1{2ν`oPp1q. Using Lemma 2.7 of Bai and Silverstein (1998), conditional on W2, 1 pνTD1{2pW2`λIpq´1D1{2ν“ 1 ptr","venue":null,"work_id":"337204da-a87c-49e7-909a-d9b2e57bce03","year":2011},"citing_paper":{"arxiv_id":"2504.15510","last_updated":"2026-06-10T01:33:24Z","snapshot_observed_at":"2026-08-16T11:22:34.392765Z","submitted_at":"2025-04-22T01:10:31Z","title":"Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses","version":3},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-16T11:31:17.378364Z"},"links":{"citing_paper":"/paper/2504.15510"},"observation_digest":"sha256:f6175dce9a111fbf8cdfcf33d32e4ea6e3c021030f35efbdc4e73d4afbcfe620","observation_id":"52f07a72-df28-4b62-84d0-46fb168c377c","resolution":{"observed_at":"2026-08-16T11:31:17.494068Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:31:17.473576Z","title":"Therefore, s1pxq“ C pρ´xq2 `C ż τąρ dGλpτq τ´x Ñ8, as xÒρ","venue":null,"work_id":"0a2efc7a-d8a4-489c-a028-fd33aed982f9","year":2024},"citing_paper":{"arxiv_id":"2504.15510","last_updated":"2026-06-10T01:33:24Z","snapshot_observed_at":"2026-08-16T11:22:34.392765Z","submitted_at":"2025-04-22T01:10:31Z","title":"Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses","version":3},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-16T11:31:17.382924Z"},"links":{"citing_paper":"/paper/2504.15510"},"observation_digest":"sha256:ff9fb8c4448b5aa584335ecb616de218eb77c4100354a0b205503247f647258f","observation_id":"68f4c7e5-6870-4b31-a1af-22cfb74939a5","resolution":{"observed_at":"2026-08-16T11:31:17.478277Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:31:17.457295Z","title":"Using Theorem 5.1 of Li (2024), there exists constants C1, C2 and ϵ such that C1 ?x´ρďfGλpxqď C2 ?x´ρ, x Ppρ,ρ `ϵq where fGλ is the density function of Gλ","venue":null,"work_id":"30aac1ef-4e7b-48bb-a648-fd4ef87a9e17","year":2024},"citing_paper":{"arxiv_id":"2504.15510","last_updated":"2026-06-10T01:33:24Z","snapshot_observed_at":"2026-08-16T11:22:34.392765Z","submitted_at":"2025-04-22T01:10:31Z","title":"Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses","version":3},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-16T11:31:17.387378Z"},"links":{"citing_paper":"/paper/2504.15510"},"observation_digest":"sha256:5cc2fdc9810872d498799100fbecedf5c27c08a7e9f5d27972d2c1594415106c","observation_id":"bad5e9c7-0701-4e4c-894c-212e964dbec7","resolution":{"observed_at":"2026-08-16T11:31:17.462892Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:31:17.724019Z","title":"Pillai, N","venue":null,"work_id":"c4be6677-6acb-4429-8e48-9deaded53dea","year":2014},"citing_paper":{"arxiv_id":"2504.15510","last_updated":"2026-06-10T01:33:24Z","snapshot_observed_at":"2026-08-16T11:22:34.392765Z","submitted_at":"2025-04-22T01:10:31Z","title":"Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses","version":3},"reference_index":197,"source":"pdf_text","source_observed_at":"2026-08-16T11:31:17.306873Z"},"links":{"citing_paper":"/paper/2504.15510"},"observation_digest":"sha256:2104aad914a01bb513fbf8c3cc0e537c5ea2c83bfd0cc5e02b4a1b93f4b69482","observation_id":"7791cb86-bae8-46c4-884d-beac592613f1","resolution":{"observed_at":"2026-08-16T11:31:17.728550Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:31:17.709565Z","title":"Ridge-regularized Largest Root Test for High-Dimensional General Linear Hypotheses","venue":null,"work_id":"7ecb384a-ba65-4da7-a7da-1dc5305dff38","year":1995},"citing_paper":{"arxiv_id":"2504.15510","last_updated":"2026-06-10T01:33:24Z","snapshot_observed_at":"2026-08-16T11:22:34.392765Z","submitted_at":"2025-04-22T01:10:31Z","title":"Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses","version":3},"reference_index":1001,"source":"pdf_text","source_observed_at":"2026-08-16T11:31:17.312019Z"},"links":{"citing_paper":"/paper/2504.15510"},"observation_digest":"sha256:a6a7bb1a1abb0182686efc598e839a1ecf24fe7d1c554c9f8a4ee39ab57d08e8","observation_id":"d5137852-438b-4917-9d4b-4b8ead605d0f","resolution":{"observed_at":"2026-08-16T11:31:17.714233Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1105.1404","last_updated":"2011-05-07T00:40:03Z","snapshot_observed_at":"2026-08-15T04:47:27.542427Z","submitted_at":"2011-05-07T00:40:03Z","title":"Geometric sensitivity of random matrix results: consequences for shrinkage estimators of covariance and related statistical methods","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1105.1404","snapshot_observed_at":"2026-08-16T11:31:17.301713Z","title":null,"venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2504.15510","last_updated":"2026-06-10T01:33:24Z","snapshot_observed_at":"2026-08-16T11:22:34.392765Z","submitted_at":"2025-04-22T01:10:31Z","title":"Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses","version":3},"reference_index":2006,"source":"pdf_text","source_observed_at":"2026-08-16T11:31:17.301713Z"},"links":{"cited_paper":"/paper/1105.1404","citing_paper":"/paper/2504.15510"},"observation_digest":"sha256:56638cdcb8c64982251a2a61f95d8a29957f00f84f401d46c63217aa93fd5704","observation_id":"0968d010-c3d0-4921-bc51-8ac28e588165","resolution":{"observed_at":"2026-08-16T11:31:17.301713Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2504.15510","last_updated":"2026-06-10T01:33:24Z","latest_version":3,"primary_category":"stat.ME","snapshot_observed_at":"2026-08-16T11:22:34.392765Z","submitted_at":"2025-04-22T01:10:31Z","title":"Ridge-Regularized Largest Root Test For High-Dimensional General Linear Hypotheses"},"reference_resolution":{"displayed":22,"state_counts":{"malformed_identifier":0,"metadata_mismatch":1,"parse_uncertain":0,"unresolved":3,"verified_exact":0,"verified_fuzzy":18},"total_outbound_references":22},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"thesis":"As of 17 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 1 inbound Pith citation observation for arXiv:2504.15510."}