{"as_of":"2026-08-16T03:48:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:ec069ff699ec8a48ca3941a142a590e07d273d76e1a01eb73604f77e482bc78e","coverage":[{"denominator":59,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":59,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T18:00:11.369547Z","state":"measured"},{"denominator":60,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":60,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-15T06:32:42.880941+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":"2026-06-26T23:22:29.661790Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-07-03T22:39:01.968853Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"cited_work":{"arxiv_id":"2507.19340","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.19340","snapshot_observed_at":"2026-07-03T22:39:01.968853Z","title":"Bucht, K","venue":null,"work_id":"705dbaa1-d763-4767-94eb-fc6fad9ff327","year":2025},"citing_paper":{"arxiv_id":"2606.17425","last_updated":"2026-06-16T02:18:45Z","snapshot_observed_at":"2026-08-14T12:22:12.153959Z","submitted_at":"2026-06-16T02:18:45Z","title":"Order statistics for edge eigenvectors of Wigner matrices","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-06-26T23:22:29.661790Z"},"links":{"cited_paper":"/paper/2507.19340","citing_paper":"/paper/2606.17425"},"observation_digest":"sha256:b69484ed33f7b385319ce79d6a06f4506ba5aabd1a4b840961c57b94dc4e359e","observation_id":"af475524-51be-43cf-9e35-5c64623fd01b","resolution":{"observed_at":"2026-07-03T22:39:01.970049Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2507.19340/citation-record","integrity":"/paper/2507.19340/integrity","json":"/paper/2507.19340/citation-record.json","paper":"/paper/2507.19340"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:12.155228Z","title":"Dyson Brownian motion for generalβ and potential at the edge","venue":null,"work_id":"432a7150-73b6-4f3e-9fff-a75af7898ce0","year":2020},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.125289Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:b87c82a4920690ff90e0739178bec3cd156944389f8b79c82ce8cbf6eab53879","observation_id":"d65bb3c5-ff32-48f6-8790-05628ab1e5d1","resolution":{"observed_at":"2026-08-15T18:00:12.159830Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:12.143554Z","title":"Edge rigidity of Dyson Brownian motion with general initial data","venue":null,"work_id":"9484534d-c2fd-4e2e-96f8-11006b514568","year":2024},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.130329Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:13f57ce8d0e09bd8c78803b613689034de03c7d1309d8be655638fa1bae80010","observation_id":"1ce3fd10-fa01-46f4-b74f-550eb9b6efcd","resolution":{"observed_at":"2026-08-15T18:00:12.147950Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:12.131971Z","title":"Localized phase for the Erdős-Rényi graph","venue":null,"work_id":"63a4fbce-badf-4897-8c35-4992eb76019b","year":2024},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.134677Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:a2e835923c98743efaaec4bedcf619051ccda0156523f8649a4e2330191ee965","observation_id":"5dd53df2-fa38-46ed-8c97-10cfdd576084","resolution":{"observed_at":"2026-08-15T18:00:12.135925Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:12.119086Z","title":"Poisson statistics and localization at the spectral edge of sparse Erdős–Rényi graphs","venue":null,"work_id":"f3f69c36-86a3-48f9-bca5-1ee36a79112a","year":2023},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.139592Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:5efb128acac4c71bf8ae0c414b2237c3be6c8fa2599ece7a8457304e298406d7","observation_id":"8abab4e5-ce4f-4b64-a661-79ddfcffde6a","resolution":{"observed_at":"2026-08-15T18:00:12.123398Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:12.107148Z","title":"Extremal eigenvalues of critical Erdős–Rényi graphs","venue":null,"work_id":"89a930a6-089b-4eac-99d9-50d2960df058","year":2021},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.143778Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:5de7be07a5d58d7a1db197ebf191219bd5ca584963b914082c1e734e478eb115","observation_id":"2a76b497-7b19-4147-bf91-d92d366f03e2","resolution":{"observed_at":"2026-08-15T18:00:12.111269Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:12.095153Z","title":"Correlated random matrices: band rigidity and edge universality","venue":null,"work_id":"4bd0fc01-dc8e-40fa-a305-3120dccaa318","year":2020},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.148237Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:d91694a41779ed63f08aae694d8f8a0b0315df93581ad69c74df08e371106fce","observation_id":"5eb8f48d-640b-4c3e-b048-909c382f96e3","resolution":{"observed_at":"2026-08-15T18:00:12.099495Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:12.082215Z","title":"Asymptotics of Tracy-Widom distributions and the total integral of a Painlevé II function","venue":null,"work_id":"d682aa11-ead6-4be4-80aa-55b50ed273b5","year":2008},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.152881Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:b6d64d229cde82a7568634663cedce5c8957e652e79984dc83e5fcfd8032565e","observation_id":"f90aff31-8010-4691-a680-2c69c7e35f9b","resolution":{"observed_at":"2026-08-15T18:00:12.087211Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:12.070725Z","title":"Edge rigidity and universality of random regular graphs of intermediate degree","venue":null,"work_id":"b1fc456d-aa2c-441b-9382-22592d743b3a","year":2020},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.156845Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:fac0b626a29088892b403f7b4d000bb1f36ebbdde49077c0d392739c70ee997a","observation_id":"0853262e-5a72-4a94-a12e-9bb357ae88ab","resolution":{"observed_at":"2026-08-15T18:00:12.074753Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:12.060103Z","title":"Largest eigenvalues of sparse inhomogeneous Erdős–Rényi graphs","venue":null,"work_id":"79aa0d23-a5bc-4e05-a061-677b3491ce5c","year":2019},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.160834Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:c55658c509527ac3dbc66875abb7537d787dfcb11e98dd17d34a04765b589557","observation_id":"33633dc4-c660-4664-bd79-38ee16353345","resolution":{"observed_at":"2026-08-15T18:00:12.063713Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:12.048252Z","title":"Spectral radii of sparse random matrices","venue":null,"work_id":"43340216-13b2-4bd3-9025-2deeadc64966","year":2020},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.165359Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:0fbbdb95cd627537867ec6ecca1d8049d61071cae7c7f1e853b38fafa88a6e7f","observation_id":"da61c0a7-5cc3-4c7e-8717-6aa5769a7088","resolution":{"observed_at":"2026-08-15T18:00:12.052719Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1601.04055","last_updated":"2018-09-10T10:48:02Z","snapshot_observed_at":"2026-08-14T22:14:26.266947Z","submitted_at":"2016-01-15T20:31:48Z","title":"Lectures on the local semicircle law for Wigner matrices","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1601.04055","snapshot_observed_at":"2026-08-15T18:00:11.169069Z","title":"Benaych-Georges and A","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.169069Z"},"links":{"cited_paper":"/paper/1601.04055","citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:be033924d384ee400b94e950c193d8040cc0d87230ec08e8eb1208b0b0acc97d","observation_id":"6c8af1b1-6832-4135-bfc9-21690c69dc0b","resolution":{"observed_at":"2026-08-15T18:00:11.169069Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:12.037202Z","title":"Hypothesis testing for automated community detection in networks","venue":null,"work_id":"d464b843-8304-4ce3-8b48-88ec69b1530e","year":2016},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.173305Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:8fc6d4907d0ea369eead228252e467676c2c9916522b4eed74b6df4a752238e1","observation_id":"95ea34f8-645a-4aa6-ace9-02eaa54be9e7","resolution":{"observed_at":"2026-08-15T18:00:12.040937Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:12.025374Z","title":"Bollobás","venue":null,"work_id":"42cb3674-6b9f-48d8-97fe-f63262a62173","year":2001},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.177159Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:c88c7b6b2afb5146864192d4751cfb6e584c7d26ec3670cdf6b2a5e0800d4174","observation_id":"8b5d9750-2078-4b54-a809-10133407e55f","resolution":{"observed_at":"2026-08-15T18:00:12.029119Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:12.013112Z","title":"Extreme gaps between eigenvalues of Wigner matrices","venue":null,"work_id":"4c573649-c95b-40ff-9dcc-71d279cd0861","year":2022},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.181212Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:4e049c8ee926ccab62999b825fdc1fc8f12119e5654696dfcd70c35fbe7e3d5c","observation_id":"847d94a1-52a4-46eb-b0bc-98da28af87b7","resolution":{"observed_at":"2026-08-15T18:00:12.016994Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:12.001265Z","title":"Edge universality of beta ensembles","venue":null,"work_id":"6486245b-a75b-46cf-955e-c1ca86158d6e","year":2014},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.185046Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:6b29a5d2b1cb8b27550bfb943ca9b7f14099e13dc71f0ffcca0faed6adfa6287","observation_id":"d7fba004-a140-45dd-ad01-06b29a6dd3d5","resolution":{"observed_at":"2026-08-15T18:00:12.005553Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:11.988707Z","title":null,"venue":null,"work_id":"5c98aba4-1f3b-46b2-9056-6158d8db04e5","year":2025},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.189040Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:e48cbdfe7b583f8997c67766a1332da5fca58e5f7b0603bd9c9eb18a3759f57e","observation_id":"29fb147f-efe9-470f-ae24-7592d0243699","resolution":{"observed_at":"2026-08-15T18:00:11.992908Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:11.975977Z","title":"DasGupta","venue":null,"work_id":"d91e1d93-7d48-4447-90f4-3206c62d182c","year":2008},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.192627Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:8eee7b7a1443f273909999167d3754c0966c4b413ece306284362b6921ff9493","observation_id":"71eb8cdf-e8c9-4718-a07c-442c096ea348","resolution":{"observed_at":"2026-08-15T18:00:11.979873Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:11.963277Z","title":"Universality at the edge of the spectrum for unitary, orthogonal, and sym- plectic ensembles of random matrices","venue":null,"work_id":"964c90a9-9175-4e43-a972-1758aaae140f","year":2007},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.196258Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:d416c201876142236531473102934c6cab87cb2184f7f631b1bd70d85071a991","observation_id":"dbfd1ac5-c6b9-4561-8afe-126e6cf9068c","resolution":{"observed_at":"2026-08-15T18:00:11.967349Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:11.951883Z","title":"Spectral statistics of Erdős-Rényi graphs I: Local semicircle law","venue":null,"work_id":"d9eee8db-910b-4301-988c-67290fced080","year":2013},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.200394Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:a3b586a85597037a519f10e6c67549e451c926fc0d27dc21170848a40517f491","observation_id":"9f0d34e3-2a65-4f33-a070-2a6b6e9f5a9b","resolution":{"observed_at":"2026-08-15T18:00:11.956082Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:11.939186Z","title":"Spectral statistics of Erdős–Rényi Graphs II: Eigen- value spacing and the extreme eigenvalues","venue":null,"work_id":"6cbb75d0-ba27-43b0-b7c0-1f2c803310b2","year":2012},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.204825Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:9f51395cd2d38a2ab53cafebe71effdb19850de9469843fbd25687feeb7389c2","observation_id":"d71af56c-ae60-4c30-a876-f6243d45859d","resolution":{"observed_at":"2026-08-15T18:00:11.944258Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:11.927798Z","title":"Erdős and H.-T","venue":null,"work_id":"a2e946ad-c989-4107-8259-c74f4e56facf","year":2017},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.208829Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:a3e5174f4cabba87b10d5a6415510fdd22754e553789900204a78d7bfc3c4efb","observation_id":"8906ead9-194a-4f1a-99cc-5a59aa7a4eb2","resolution":{"observed_at":"2026-08-15T18:00:11.931885Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:11.914516Z","title":"Rigidity of eigenvalues of generalized Wigner matrices","venue":null,"work_id":"4efc8123-56a3-4b8d-82a7-974a9f6b1b07","year":2012},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.212688Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:f74c86ca5e58774984194c8182d7b7c833a722c31df98599ad0217333ba44741","observation_id":"10cf9522-e78f-42d9-bb6a-24b317122934","resolution":{"observed_at":"2026-08-15T18:00:11.918685Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:11.900963Z","title":"Exploring Network Structure, Dynamics, and Function using NetworkX","venue":null,"work_id":"28863f37-94f6-4934-80c4-bb0fd37c90a1","year":2008},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.216707Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:f78c4b70da0c3595405565c972977251449bf893b0ecd27adb9c563ecb0a4279","observation_id":"3005de7c-7316-4ca6-8369-8b4a203d34be","resolution":{"observed_at":"2026-08-15T18:00:11.905496Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:11.886410Z","title":"Spectral gap and edge universality of dense random regular graphs","venue":null,"work_id":"226ca819-e605-4d9b-ad21-96c0709602b7","year":2024},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.220067Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:5d0795977f9873b1e74e681d1ad06e1775f495a4a55194bb49aae9efd99eac78","observation_id":"42e8bbc4-be3f-4cf9-885d-b37c449629f5","resolution":{"observed_at":"2026-08-15T18:00:11.891456Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:11.871569Z","title":"Fluctuations of extreme eigenvalues of sparse Erdős-Rényi graphs","venue":null,"work_id":"824ac832-76cd-4446-95e9-485de5076452","year":2021},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.224638Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:065a75d33267c3f3338b070a75af5d19ab6379db32c05edc1a050e3f9c51b1d2","observation_id":"6a189440-8bce-429c-8350-9cc69463423d","resolution":{"observed_at":"2026-08-15T18:00:11.875677Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:11.859655Z","title":"Mesoscopic eigenvalue statistics of Wigner matrices","venue":null,"work_id":"228285bc-1d32-4d07-857f-cb8c13dc68d0","year":2017},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.228273Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:a17f7caa053b51b07f02e97f9f0632d999e3181a330d9699ec9ee03ea0453a02","observation_id":"fb28569a-aba3-4033-b70a-1d2a3b5f2688","resolution":{"observed_at":"2026-08-15T18:00:11.863792Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:11.846799Z","title":"The spectral edge of constant degree Erdős-Rényi graphs","venue":null,"work_id":"d6044628-5da0-47e9-8c75-b34b16bd8dfe","year":2025},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.231986Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:542c9355b934787fd5ef3d621fd16f6ae713370233a037254165702ba101920c","observation_id":"502857f7-38bf-482a-8207-9d0ba3b085b4","resolution":{"observed_at":"2026-08-15T18:00:11.851206Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:11.835177Z","title":"Transition from Tracy–Widom to Gaussian fluctuations of extremal eigenvalues of sparse Erdős–Rényi graphs","venue":null,"work_id":"17036f68-04b3-4ca7-8f4e-63149b2aa90f","year":2020},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.235934Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:901f45edb6cd8917d42059a42686ef2931acfd9ec8d9e66a3654124a5c1e6890","observation_id":"63eeb045-b6df-4ea3-81f5-5d103ef5fa2c","resolution":{"observed_at":"2026-08-15T18:00:11.839304Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2405.12161","last_updated":"2024-05-20T16:42:41Z","snapshot_observed_at":"2026-08-13T00:03:39.109927Z","submitted_at":"2024-05-20T16:42:41Z","title":"Optimal Eigenvalue Rigidity of Random Regular Graphs","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.12161","snapshot_observed_at":"2026-08-15T18:00:11.239361Z","title":"Optimal eigenvalue rigidity of random regular graphs","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.239361Z"},"links":{"cited_paper":"/paper/2405.12161","citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:dd2af144f072e419b8c2e31f66840fb10a11586d3b119d6d6552cffd29d348c6","observation_id":"ee5810d2-ec2a-45e5-80a1-0d6f4bd79ff7","resolution":{"observed_at":"2026-08-15T18:00:11.239361Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2412.20263","last_updated":"2025-02-02T22:46:43Z","snapshot_observed_at":"2026-08-14T04:52:20.763004Z","submitted_at":"2024-12-28T20:34:12Z","title":"Ramanujan Property and Edge Universality of Random Regular Graphs","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.20263","snapshot_observed_at":"2026-08-15T18:00:11.243215Z","title":"Ramanujan property and edge universality of randomregular graphs","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.243215Z"},"links":{"cited_paper":"/paper/2412.20263","citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:89985227a41fb1d151684884dccfb4637c33a1b81ae459749b9e87a968f644b6","observation_id":"e6fa4640-26f9-4f4a-8760-75c9db555120","resolution":{"observed_at":"2026-08-15T18:00:11.243215Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2305.01428","last_updated":"2023-06-09T13:08:56Z","snapshot_observed_at":"2026-08-13T11:50:46.456477Z","submitted_at":"2023-05-02T13:58:10Z","title":"Edge Universality of Random Regular Graphs of Growing Degrees","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2305.01428","snapshot_observed_at":"2026-08-15T18:00:11.248108Z","title":"Edge universality of random regular graphs of growing degrees","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.248108Z"},"links":{"cited_paper":"/paper/2305.01428","citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:b53b1a43c4ed913791469fd7459a7800b7244bb8c352352f3953f3d5ad18365d","observation_id":"a4633c67-6b9c-4bfc-8bf2-4f952f86838c","resolution":{"observed_at":"2026-08-15T18:00:11.248108Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2206.06580","last_updated":"2023-05-04T00:21:52Z","snapshot_observed_at":"2026-08-13T15:24:24.877476Z","submitted_at":"2022-06-14T03:46:00Z","title":"Edge Universality of Sparse Random Matrices","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2206.06580","snapshot_observed_at":"2026-08-15T18:00:11.252055Z","title":"Edgeuniversalityofsparserandommatrices","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.252055Z"},"links":{"cited_paper":"/paper/2206.06580","citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:ae8efe64e924f331908ba25ec2848c20be2d5876b920d453205e18d5901496b2","observation_id":"82d88b01-c929-49af-aea2-28c7e12c1260","resolution":{"observed_at":"2026-08-15T18:00:11.252055Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:11.820295Z","title":"Spectrum of randomd-regular graphs up to the edge","venue":null,"work_id":"fd4e97e4-b477-48a6-a846-835622f8df61","year":2024},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.256201Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:de9dbc5a34ff13c00f47f9b26f4a2a2930d6248e7edd349651a612e015edea7b","observation_id":"94d3ef5d-26ba-47e8-8a6b-09ae0a839ab4","resolution":{"observed_at":"2026-08-15T18:00:11.824740Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:11.801980Z","title":"Janson, T","venue":null,"work_id":"8b04dc8a-3290-4ed6-80cb-a42b08bcbb71","year":2000},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.260407Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:6bd5be4b0d27880f9126f5618ed3545d864141054b552f1c41784a807c2f34f8","observation_id":"28ff171c-d7c8-4fa9-9f3b-0d0e68a723c8","resolution":{"observed_at":"2026-08-15T18:00:11.807576Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:11.788056Z","title":"Fast approach to the Tracy-Widom law at the edge of GOE and GUE","venue":null,"work_id":"d1b78e87-94b5-41cc-8e70-24eee507a06e","year":2012},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.264387Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:00e121799eba66e4560c5774ddc189472fb52324b08eb1211aad1f675c1d9926","observation_id":"064a96bd-698e-438a-8e6e-ab91813d2ad3","resolution":{"observed_at":"2026-08-15T18:00:11.792701Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:11.774664Z","title":"VF2++—an improved subgraph isomorphism algorithm","venue":null,"work_id":"79af9778-59a6-460a-b45f-4708503d4af1","year":2018},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.268400Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:0e158abac7fbac7cc4e417402c047f58ca7582c37f413286e3147f2d2d228035","observation_id":"7daf0f41-7224-4026-97e3-5c5d6fc0a44c","resolution":{"observed_at":"2026-08-15T18:00:11.778879Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:11.761991Z","title":"Sparse random matrices: spectral edge and statistics of rooted trees","venue":null,"work_id":"d9b72248-6e65-4a4e-9aec-21df3bbb8b12","year":2001},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.272473Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:8f31cb2314b0574234da23c4b68f581847ee4f08c052b2d4f0cdff3ad11c72ae","observation_id":"cdde830e-9217-45f7-800b-059954ab66b5","resolution":{"observed_at":"2026-08-15T18:00:11.766560Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:11.749774Z","title":"Anisotropic local laws for random matrices","venue":null,"work_id":"d200f5ec-73fb-4c2f-a41a-3c8fb92d0175","year":2017},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.276850Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:3072bbdd8edabae61b7c09dfc858fb6547e5308add24ea85cf728a995a71185b","observation_id":"a47d26ac-c894-4c90-a72f-3dbf6e3470bc","resolution":{"observed_at":"2026-08-15T18:00:11.754045Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:11.737761Z","title":"Köbler, U","venue":null,"work_id":"5cf3a885-25d0-4fdc-a460-bc411977669f","year":1993},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.281213Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:63f94cae14086a94286dcd584cec3cee2a729f311d58e5c1485523a63d212193","observation_id":"b43a5cfc-884c-4b0f-8fff-343411452443","resolution":{"observed_at":"2026-08-15T18:00:11.742171Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1712.03881","last_updated":"2017-12-11T16:45:41Z","snapshot_observed_at":"2026-08-14T20:04:51.313846Z","submitted_at":"2017-12-11T16:45:41Z","title":"Edge statistics of Dyson Brownian motion","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1712.03881","snapshot_observed_at":"2026-08-15T18:00:11.286795Z","title":"EdgestatisticsofDysonBrownianmotion","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.286795Z"},"links":{"cited_paper":"/paper/1712.03881","citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:c08ee9c53315d1fa78742e42caf9486777bf07b3623a0bbe393e7fb221e7dcf7","observation_id":"d5c972cc-b1bd-46af-9cf0-613c148d51bf","resolution":{"observed_at":"2026-08-15T18:00:11.286795Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:11.723070Z","title":"The dimension-free structure of nonhomogeneous random matrices","venue":null,"work_id":"11d933e7-50cb-4306-bffe-911715f0a68b","year":2018},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.292365Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:3c1753f6f1bd1427d89588aa6dc58f42f3c951660a30b3e67e93ce43c285d696","observation_id":"9f3e8ca1-474b-40a8-a31c-b2da52b77631","resolution":{"observed_at":"2026-08-15T18:00:11.728429Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2108.11634","last_updated":"2023-06-07T11:19:43Z","snapshot_observed_at":"2026-07-06T11:41:41.795110Z","submitted_at":"2021-08-26T08:02:12Z","title":"Higher order fluctuations of extremal eigenvalues of sparse random matrices","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.11634","snapshot_observed_at":"2026-08-15T18:00:11.296561Z","title":"Higher order fluctuations of extremal eigenvalues of sparse random matrices","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.296561Z"},"links":{"cited_paper":"/paper/2108.11634","citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:309be101893c6462283b78bf59be96b60c8b9b8eae2ff1f5af5b7f19716dbf11","observation_id":"38092677-2487-472b-9f0c-957e72beefd4","resolution":{"observed_at":"2026-08-15T18:00:11.296561Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:11.707983Z","title":"Edge universality for deformed Wigner matrices","venue":null,"work_id":"c039084d-be76-4820-888d-c2b2b91ffb42","year":2015},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.300908Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:aa7bdd302b04ff7588fe531326ee9af5c70781b941d456994b1a5d5678df523a","observation_id":"66ef6070-23d4-437a-a0f9-333e3d34fc3f","resolution":{"observed_at":"2026-08-15T18:00:11.712321Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:11.692052Z","title":"Local law and Tracy-Widom limit for sparse random matrices","venue":null,"work_id":"e2b10941-b230-4f37-a160-a848e9675d1c","year":2018},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.304896Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:1ca7201445d53d58502cd920b0f8821fdf62b76856d8badf1c6ab495415a42ee","observation_id":"75b5a787-7d4b-432e-b670-4a90b3a83b98","resolution":{"observed_at":"2026-08-15T18:00:11.696895Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:11.677121Z","title":"A necessary and sufficient condition for edge universality of Wigner matrices","venue":null,"work_id":"7f310b02-8572-412a-9f8f-66973331a777","year":2014},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.309712Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:175d8ed73535c3d1b579a9aa74d345593b62b0df0d14c78b588cd520bc13c4a3","observation_id":"60521d36-5a7a-4c41-8ffd-75a981e51919","resolution":{"observed_at":"2026-08-15T18:00:11.683237Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:11.663915Z","title":"A goodness-of-fit test for stochastic block models","venue":null,"work_id":"8387b25c-405b-4e3f-a812-ec26586e8488","year":2016},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.313654Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:137b14ce88213ab3bcca2226bb257c12ec162aa4b9dd644f6664d3509261e065","observation_id":"2642d67e-c139-45a8-b280-8d025017dc2b","resolution":{"observed_at":"2026-08-15T18:00:11.668715Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2401.00492","last_updated":"2025-06-03T07:35:20Z","snapshot_observed_at":"2026-08-13T04:50:48.228308Z","submitted_at":"2023-12-31T13:25:37Z","title":"Edge statistics for random band matrices","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2401.00492","snapshot_observed_at":"2026-08-15T18:00:11.317592Z","title":"Edgestatisticsforrandombandmatrices","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.317592Z"},"links":{"cited_paper":"/paper/2401.00492","citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:d2d723f393d73e36e7d27afac5aca63900cca2375745aaae7a0fd9609a8be3fe","observation_id":"e4b09439-ddc8-4c34-84b8-bcc8a57b6001","resolution":{"observed_at":"2026-08-15T18:00:11.317592Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:11.652392Z","title":"Algorithm 1021: SPEX Left LU, exactly solving sparse linear systems via a sparse left-looking integer-preserving LU factorization","venue":null,"work_id":"5643a7ae-cb83-463e-8a1e-aca06656028a","year":2022},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.322472Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:7ba3dfcead49cc99f0beda7436e5f7295af9259fd2fd7bf3948aa37ef36e3fbe","observation_id":"683cab5d-5957-4c9b-8b2d-c432b9a74a3f","resolution":{"observed_at":"2026-08-15T18:00:11.656481Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:11.640959Z","title":"On the lower bound of the spectral norm of symmetric random matrices with independent entries","venue":null,"work_id":"7a20262a-db99-4b99-8175-a9bdd9a3a011","year":2008},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.327175Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:7d55a7bbcb30dda3624ab4b097c7ad48d5cc06b796c8a92c3c0327c19d825775","observation_id":"9760bbf4-f729-40ab-a480-858f481cbb58","resolution":{"observed_at":"2026-08-15T18:00:11.644965Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:11.629054Z","title":"Wigner random matrices with non-symmetrically distributed entries","venue":null,"work_id":"e4aff0f5-fd3e-44a6-bd7f-4a2ebdaaad98","year":2007},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.332511Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:699ffdf125ada8ce033e7a482f8aa01c358b4b813fdcdfac01c94116e24c0687","observation_id":"2606230b-4486-4203-9b13-ece1f702a76f","resolution":{"observed_at":"2026-08-15T18:00:11.633770Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:11.617546Z","title":"Convergence rate to the Tracy-Widom laws for the largest eigenvalue of Wigner matrices","venue":null,"work_id":"605ed9bb-4962-4e4f-91af-f73e6ddfddda","year":2022},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.337098Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:86b8d5f3e142be51d754b0c6aa57849b33d586053b140b5ca334d32e47b3b87c","observation_id":"c858ebda-73c3-40b2-b74a-22a94462a754","resolution":{"observed_at":"2026-08-15T18:00:11.621644Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:11.604343Z","title":"Quantitative Tracy-Widom laws for the largest eigenvalue of generalized Wigner matrices","venue":null,"work_id":"3d91ff32-186e-435a-92dd-8b5d70d74923","year":2023},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.341893Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:b9c0a776ab70571cb9e9b992e84ae5988e087da317f02895c998a1087a701e1a","observation_id":"61cd4e9d-d108-49cd-bca1-a26a5eab8100","resolution":{"observed_at":"2026-08-15T18:00:11.609059Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:11.592223Z","title":"The spectral edge of some random band matrices","venue":null,"work_id":"91e32f62-5ba0-42a3-947d-8b0a1a5c9da1","year":2010},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.346036Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:8e1d11b831af665400c7237fc1c09100781d2c54da0faae19eceaef68775f439","observation_id":"1704820a-c8d8-47e4-ba25-2fba7ef66018","resolution":{"observed_at":"2026-08-15T18:00:11.596598Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:11.576753Z","title":"Universality at the edge of the spectrum in Wigner random matrices","venue":null,"work_id":"55347a0c-00d9-420d-b1a8-a45a3a2007d3","year":1999},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.350930Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:147532f27f3e1e596b90933102884b6a623bdc45bb0d0edf8cd59773f25ccb38","observation_id":"e7c1056c-3f05-4da8-9818-3710e63cf44c","resolution":{"observed_at":"2026-08-15T18:00:11.581358Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:11.562825Z","title":"Random matrices: universality of local eigenvalue statistics up to the edge","venue":null,"work_id":"25dff254-ec90-48e7-88f7-37efc3ba7b1e","year":2010},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.354792Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:7b6949fa89da0a7a22b2341a6053059ecf4671b753711901cb190464971bb7b5","observation_id":"a6e144fc-f266-4908-8ea5-7439b6d2c6dc","resolution":{"observed_at":"2026-08-15T18:00:11.567034Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:11.548036Z","title":"Outliers in spectrum of sparse Wigner matrices","venue":null,"work_id":"8b24ac35-b0ee-4be3-ad8b-ec12a6e475d5","year":2021},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.358441Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:1936cf4aebd89d44c6327a11c15495652ffae3323aa76f159c7c9f6e66aaf1b6","observation_id":"79249518-9e02-4a44-aaf7-0f04fe4e1071","resolution":{"observed_at":"2026-08-15T18:00:11.553266Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:11.531224Z","title":"Level-spacing distributions and the Airy kernel","venue":null,"work_id":"a2279386-03a4-4acd-8943-d5c621ed271d","year":1994},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.362044Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:0f72c3e29bb1d1a00efd20d0f1fff37c2ecd7fc50a880beb14f1f38f730300b9","observation_id":"572efe1a-c97d-4e1d-9c04-6d2b03daefc3","resolution":{"observed_at":"2026-08-15T18:00:11.536773Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:11.515377Z","title":"On orthogonal and symplectic matrix ensembles","venue":null,"work_id":"e09c632b-be4b-4d8e-b228-525488d1e5f4","year":1996},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.365663Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:0b82b4b715573b9b0f4e9212c5514eb289c3279ca3103f95f2c7021b895c4d49","observation_id":"fe49556a-105d-4501-8da5-71288a164338","resolution":{"observed_at":"2026-08-15T18:00:11.520903Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T18:00:11.499911Z","title":"Spectral norm of random matrices","venue":null,"work_id":"1c741768-35b0-4bdb-985d-d7780142b264","year":2007},"citing_paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-15T18:00:11.369547Z"},"links":{"citing_paper":"/paper/2507.19340"},"observation_digest":"sha256:11aba1b927f0a5ac98966847bb3e3821c98ce8c46a05c192c2490049eeea8713","observation_id":"44dca746-cca6-4d15-a24e-a8891125098d","resolution":{"observed_at":"2026-08-15T18:00:11.506404Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.19340","last_updated":"2025-07-25T14:50:07Z","latest_version":1,"primary_category":"math.PR","snapshot_observed_at":"2026-08-15T17:52:37.534760Z","submitted_at":"2025-07-25T14:50:07Z","title":"Quantitative Tracy-Widom laws for sparse random matrices"},"reference_resolution":{"displayed":59,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":9,"verified_exact":0,"verified_fuzzy":50},"total_outbound_references":59},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"thesis":"As of 16 August 2026, this Paper Citation Record lists 59 of 59 outbound references and 1 inbound Pith citation observation for arXiv:2507.19340."}