{"as_of":"2026-08-20T15:22:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:2e8b81a3e546ae92a22e35056dc633028c8f71802553f0204142516a964a8097","coverage":[{"denominator":37,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":37,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-16T11:18:35.950200Z","state":"measured"},{"denominator":39,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":39,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-20T06:33:59.587034+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-23T01:08:13.915792Z","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":"2026-05-23T01:12:21.467484Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2504.15992","last_updated":"2025-04-22T15:54:32Z","snapshot_observed_at":"2026-08-18T22:56:04.352071Z","submitted_at":"2025-04-22T15:54:32Z","title":"Repeated singular values of a random symmetric matrix and decoupled singular value estimates","version":1},"cited_work":{"arxiv_id":"2504.15992","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2504.15992","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Repeated singular values of a random symmetric matrix and decoupled singular value estimates","venue":null,"work_id":"5a3c043d-9cb9-4477-bcae-17c6841d5b76","year":2025},"citing_paper":{"arxiv_id":"2503.08139","last_updated":"2026-04-13T13:50:09Z","snapshot_observed_at":"2026-07-06T20:50:27.661417Z","submitted_at":"2025-03-11T07:59:07Z","title":"The eigenvalue gap of inhomogeneous symmetric discrete random matrix","version":4},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-05-23T01:08:13.915792Z"},"links":{"cited_paper":"/paper/2504.15992","citing_paper":"/paper/2503.08139"},"observation_digest":"sha256:6b0dcba4048db186b860260cf502fff9d1f4dc5f723f14aa9bceb79d413670fb","observation_id":"0ed3fc30-d220-4476-b42a-a77b6787a678","resolution":{"observed_at":"2026-05-23T01:12:21.469859Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2504.15992","last_updated":"2025-04-22T15:54:32Z","snapshot_observed_at":"2026-08-18T22:56:04.352071Z","submitted_at":"2025-04-22T15:54:32Z","title":"Repeated singular values of a random symmetric matrix and decoupled singular value estimates","version":1},"cited_work":{"arxiv_id":"2504.15992","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2504.15992","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Repeated singular values of a random symmetric matrix and decoupled singular value estimates","venue":null,"work_id":"5a3c043d-9cb9-4477-bcae-17c6841d5b76","year":2025},"citing_paper":{"arxiv_id":"2506.01155","last_updated":"2026-05-06T19:18:15Z","snapshot_observed_at":"2026-08-06T23:23:31.323037Z","submitted_at":"2025-06-01T20:27:54Z","title":"On the rank of a random symmetric matrix in the large deviation regime","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-05-19T12:01:13.073295Z"},"links":{"cited_paper":"/paper/2504.15992","citing_paper":"/paper/2506.01155"},"observation_digest":"sha256:2406ddaaee305f1997f66f2047d893d051e23e8177f4da9ad9b2e48792c96769","observation_id":"8b58ace3-9e3a-4c6d-9c9f-4f6acfb9d9ab","resolution":{"observed_at":"2026-05-19T12:02:16.719942Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2504.15992/citation-record","integrity":"/paper/2504.15992/integrity","json":"/paper/2504.15992/citation-record.json","paper":"/paper/2504.15992"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:18:37.993223Z","title":"Extreme gaps between eigenvalues of Wig ner matrices","venue":null,"work_id":"c9c7dee4-668d-4b45-afde-1677608e201c","year":2021},"citing_paper":{"arxiv_id":"2504.15992","last_updated":"2025-04-22T15:54:32Z","snapshot_observed_at":"2026-08-18T22:56:04.352071Z","submitted_at":"2025-04-22T15:54:32Z","title":"Repeated singular values of a random symmetric matrix and decoupled singular value estimates","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-16T11:18:35.187978Z"},"links":{"citing_paper":"/paper/2504.15992"},"observation_digest":"sha256:9b1333fb8ef18f5573ce7b5424006c6e37636b17558d4d78840077169df6a7b6","observation_id":"8dd0b1b3-c973-4bce-97ba-af1a4985fbae","resolution":{"observed_at":"2026-08-16T11:18:37.996497Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:18:37.778286Z","title":"Fixed energy universality for gene ralized Wigner matrices","venue":null,"work_id":"e48ae8c8-9c8d-4408-914b-0ccb93215137","year":2016},"citing_paper":{"arxiv_id":"2504.15992","last_updated":"2025-04-22T15:54:32Z","snapshot_observed_at":"2026-08-18T22:56:04.352071Z","submitted_at":"2025-04-22T15:54:32Z","title":"Repeated singular values of a random symmetric matrix and decoupled singular value estimates","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-16T11:18:35.290392Z"},"links":{"citing_paper":"/paper/2504.15992"},"observation_digest":"sha256:62147f863b608b32e059f601f7a0b2011999be471a8de3ef13e509293f065cdf","observation_id":"7030e257-4dcf-4222-9622-a991b125a27d","resolution":{"observed_at":"2026-08-16T11:18:37.931749Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:18:35.399626Z","title":"On the singularity of random symme tric matrices","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2504.15992","last_updated":"2025-04-22T15:54:32Z","snapshot_observed_at":"2026-08-18T22:56:04.352071Z","submitted_at":"2025-04-22T15:54:32Z","title":"Repeated singular values of a random symmetric matrix and decoupled singular value estimates","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-16T11:18:35.399626Z"},"links":{"citing_paper":"/paper/2504.15992"},"observation_digest":"sha256:4a0d69c5bd285f81dd391b032a892876efd097c1a17bf464024a588d2bd2a324","observation_id":"faab2a31-831c-490c-a478-0aa1b36c263f","resolution":{"observed_at":"2026-08-16T11:18:35.399626Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:18:35.402907Z","title":"Singularity of random symmetric m atrices revisited","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2504.15992","last_updated":"2025-04-22T15:54:32Z","snapshot_observed_at":"2026-08-18T22:56:04.352071Z","submitted_at":"2025-04-22T15:54:32Z","title":"Repeated singular values of a random symmetric matrix and decoupled singular value estimates","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-16T11:18:35.402907Z"},"links":{"citing_paper":"/paper/2504.15992"},"observation_digest":"sha256:21c22b81488d3478bf746c789cdbdaca5e5053ac258cb088f6be1def776ab365","observation_id":"83f64423-5b56-453c-aef6-b63588f54589","resolution":{"observed_at":"2026-08-16T11:18:35.402907Z","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":"2026-08-16T11:18:37.755287Z","title":"The least singular value of a rando m symmetric matrix","venue":null,"work_id":"c4f8d4fc-9889-49fc-8801-427f2e26d2eb","year":2024},"citing_paper":{"arxiv_id":"2504.15992","last_updated":"2025-04-22T15:54:32Z","snapshot_observed_at":"2026-08-18T22:56:04.352071Z","submitted_at":"2025-04-22T15:54:32Z","title":"Repeated singular values of a random symmetric matrix and decoupled singular value estimates","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-16T11:18:35.406996Z"},"links":{"citing_paper":"/paper/2504.15992"},"observation_digest":"sha256:5465066372b05419e65797b54e23a6236c38eedcf8717cb75d213eda0898ecab","observation_id":"207131c3-31e9-49e0-b9f7-433f34cd7682","resolution":{"observed_at":"2026-08-16T11:18:37.759751Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:18:37.743195Z","title":"The singularity probability of a r andom symmetric matrix is exponentially small","venue":null,"work_id":"03ac18f1-3356-4ee2-91ac-635f9ff2b081","year":2025},"citing_paper":{"arxiv_id":"2504.15992","last_updated":"2025-04-22T15:54:32Z","snapshot_observed_at":"2026-08-18T22:56:04.352071Z","submitted_at":"2025-04-22T15:54:32Z","title":"Repeated singular values of a random symmetric matrix and decoupled singular value estimates","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-16T11:18:35.411560Z"},"links":{"citing_paper":"/paper/2504.15992"},"observation_digest":"sha256:e5091fb34364e588a0833bf9a95938119dbdbbb22b319885ea56e78b6b3ef1c0","observation_id":"7f4ce699-5a1d-4ff1-96dd-322d464892b1","resolution":{"observed_at":"2026-08-16T11:18:37.748469Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2501.00234","last_updated":"2025-03-16T22:38:46Z","snapshot_observed_at":"2026-08-14T03:02:15.836071Z","submitted_at":"2024-12-31T03:00:04Z","title":"Eigenvalue gaps of the Laplacian of random graphs","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2501.00234","snapshot_observed_at":"2026-08-16T11:18:35.415309Z","title":"Eigenvalue gaps of the Lap lacian of random graphs","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2504.15992","last_updated":"2025-04-22T15:54:32Z","snapshot_observed_at":"2026-08-18T22:56:04.352071Z","submitted_at":"2025-04-22T15:54:32Z","title":"Repeated singular values of a random symmetric matrix and decoupled singular value estimates","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-16T11:18:35.415309Z"},"links":{"cited_paper":"/paper/2501.00234","citing_paper":"/paper/2504.15992"},"observation_digest":"sha256:d95440bca89aea353cd918b7b541b6934fc5f93646a2d75a94041429b45aed30","observation_id":"e8a47ed6-baae-472f-8890-340f6438e520","resolution":{"observed_at":"2026-08-16T11:18:35.415309Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:18:35.419215Z","title":"Gaps between Singular Val ues of Sample Covariance Matrices","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2504.15992","last_updated":"2025-04-22T15:54:32Z","snapshot_observed_at":"2026-08-18T22:56:04.352071Z","submitted_at":"2025-04-22T15:54:32Z","title":"Repeated singular values of a random symmetric matrix and decoupled singular value estimates","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-16T11:18:35.419215Z"},"links":{"citing_paper":"/paper/2504.15992"},"observation_digest":"sha256:847736009cdafb2a685fd64a2df91b3fa37f4338b61ed45c9ab7a5899941b4f5","observation_id":"9043e5af-7c17-42e0-8c58-84485b458b35","resolution":{"observed_at":"2026-08-16T11:18:35.419215Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:18:35.423181Z","title":"Eigenvector decorrelation fo r random matrices","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2504.15992","last_updated":"2025-04-22T15:54:32Z","snapshot_observed_at":"2026-08-18T22:56:04.352071Z","submitted_at":"2025-04-22T15:54:32Z","title":"Repeated singular values of a random symmetric matrix and decoupled singular value estimates","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-16T11:18:35.423181Z"},"links":{"citing_paper":"/paper/2504.15992"},"observation_digest":"sha256:133e0a655c24fb43040c1154d5fce99f7710dc87b9e24ede3e41fab7f5b6549d","observation_id":"ed7a3536-1fe8-411b-b8f8-256aa0a0f376","resolution":{"observed_at":"2026-08-16T11:18:35.423181Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:18:35.427921Z","title":"Random symm etric matrices are al- most surely nonsingular","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2504.15992","last_updated":"2025-04-22T15:54:32Z","snapshot_observed_at":"2026-08-18T22:56:04.352071Z","submitted_at":"2025-04-22T15:54:32Z","title":"Repeated singular values of a random symmetric matrix and decoupled singular value estimates","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-16T11:18:35.427921Z"},"links":{"citing_paper":"/paper/2504.15992"},"observation_digest":"sha256:3179d87dc56210829d05533d64a30b7c3e4bd8d35171740c8265fa2712628845","observation_id":"d630201d-b172-493b-9881-1e0f71a97515","resolution":{"observed_at":"2026-08-16T11:18:35.427921Z","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":"2026-08-16T11:18:37.727636Z","title":"Universality of Wigner random matrices: a survey of recent results","venue":null,"work_id":"74a49d00-4bd3-4c20-851b-6c7716177041","year":2011},"citing_paper":{"arxiv_id":"2504.15992","last_updated":"2025-04-22T15:54:32Z","snapshot_observed_at":"2026-08-18T22:56:04.352071Z","submitted_at":"2025-04-22T15:54:32Z","title":"Repeated singular values of a random symmetric matrix and decoupled singular value estimates","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-16T11:18:35.432031Z"},"links":{"citing_paper":"/paper/2504.15992"},"observation_digest":"sha256:fb0d9e2f63f00b26478b3d1209efbff9cd4b406f6ce683a71d664958506ff795","observation_id":"a15dac25-e57d-4580-8523-4c551f0a4c55","resolution":{"observed_at":"2026-08-16T11:18:37.731058Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:18:37.441962Z","title":"Wegner estimate and level re- pulsion for Wigner random matrices","venue":null,"work_id":"250ff439-d092-4785-91dc-d3a1bbde14ad","year":2010},"citing_paper":{"arxiv_id":"2504.15992","last_updated":"2025-04-22T15:54:32Z","snapshot_observed_at":"2026-08-18T22:56:04.352071Z","submitted_at":"2025-04-22T15:54:32Z","title":"Repeated singular values of a random symmetric matrix and decoupled singular value estimates","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-16T11:18:35.435478Z"},"links":{"citing_paper":"/paper/2504.15992"},"observation_digest":"sha256:91a5205c88b3f5abd375c954c07ee613ef8373ca4f90014c9114bb5b190f2286","observation_id":"95c646c8-0e0a-4c90-81a9-f7deb2f9b84a","resolution":{"observed_at":"2026-08-16T11:18:37.597604Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:18:35.438962Z","title":"Rigidity of eigenvalues of generalized Wigner matrices","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2504.15992","last_updated":"2025-04-22T15:54:32Z","snapshot_observed_at":"2026-08-18T22:56:04.352071Z","submitted_at":"2025-04-22T15:54:32Z","title":"Repeated singular values of a random symmetric matrix and decoupled singular value estimates","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-16T11:18:35.438962Z"},"links":{"citing_paper":"/paper/2504.15992"},"observation_digest":"sha256:6b3a0f8d5fd2bee5c19ab84a667d7c8a4c087f6b9d38cc0a26b0b667ac70ee46","observation_id":"85a98696-fecc-43b5-94f4-61eea091bf84","resolution":{"observed_at":"2026-08-16T11:18:35.438962Z","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":"2026-08-16T11:18:37.203916Z","title":"On the Kolmogorov-Rogozin ineq uality for the concentration function","venue":null,"work_id":"7fc6b59a-0e19-4671-b356-9e0253082cdc","year":1966},"citing_paper":{"arxiv_id":"2504.15992","last_updated":"2025-04-22T15:54:32Z","snapshot_observed_at":"2026-08-18T22:56:04.352071Z","submitted_at":"2025-04-22T15:54:32Z","title":"Repeated singular values of a random symmetric matrix and decoupled singular value estimates","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-16T11:18:35.516617Z"},"links":{"citing_paper":"/paper/2504.15992"},"observation_digest":"sha256:85292798b45cac947588a7d663cd7a8050a720f8d870f6b485d4cc55363b93d3","observation_id":"7350cd3b-d6a4-4460-8472-a2aabc1c58d7","resolution":{"observed_at":"2026-08-16T11:18:37.331787Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:18:35.596330Z","title":"A universality result for the smallest eigenvalues of certain sample covariance matrices","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2504.15992","last_updated":"2025-04-22T15:54:32Z","snapshot_observed_at":"2026-08-18T22:56:04.352071Z","submitted_at":"2025-04-22T15:54:32Z","title":"Repeated singular values of a random symmetric matrix and decoupled singular value estimates","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-16T11:18:35.596330Z"},"links":{"citing_paper":"/paper/2504.15992"},"observation_digest":"sha256:b3637bc27702f79d7f7478014eedc2ffbe63e2a2a9fc4acb37fe8f8c2ffed14c","observation_id":"66d2539f-c541-4888-8de7-f694b987d33d","resolution":{"observed_at":"2026-08-16T11:18:35.596330Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:18:35.659401Z","title":"Singularity of random sy mmetric matrices—a com- binatorial approach to improved bounds","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2504.15992","last_updated":"2025-04-22T15:54:32Z","snapshot_observed_at":"2026-08-18T22:56:04.352071Z","submitted_at":"2025-04-22T15:54:32Z","title":"Repeated singular values of a random symmetric matrix and decoupled singular value estimates","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-16T11:18:35.659401Z"},"links":{"citing_paper":"/paper/2504.15992"},"observation_digest":"sha256:ac742a9c68a2756fe9dff0f85a01c86ed9a3193052db007b0efd17d6af0fcdb7","observation_id":"de1c3b8c-3d25-45ad-81c2-ca5652b71079","resolution":{"observed_at":"2026-08-16T11:18:35.659401Z","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":"2026-08-16T11:18:37.181754Z","title":"Large deviations for the largest eigenvalue of Rademacher matrices","venue":null,"work_id":"e7034fcc-f60e-4b98-931e-dde47b96c3b4","year":2020},"citing_paper":{"arxiv_id":"2504.15992","last_updated":"2025-04-22T15:54:32Z","snapshot_observed_at":"2026-08-18T22:56:04.352071Z","submitted_at":"2025-04-22T15:54:32Z","title":"Repeated singular values of a random symmetric matrix and decoupled singular value estimates","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-16T11:18:35.683963Z"},"links":{"citing_paper":"/paper/2504.15992"},"observation_digest":"sha256:4e638adbddda132140160fb10c3465283e5225ee8bd4e69c8972b018c566364f","observation_id":"df707414-e1a3-46df-8b4c-c6cf73874046","resolution":{"observed_at":"2026-08-16T11:18:37.185357Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2502.13819","last_updated":"2025-03-01T18:38:23Z","snapshot_observed_at":"2026-08-16T19:02:51.159202Z","submitted_at":"2025-02-19T15:31:35Z","title":"Simplicity of singular value spectrum of random matrices and two-point quantitative invertibility","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.13819","snapshot_observed_at":"2026-08-16T11:18:35.688380Z","title":"Simplicity of singular value spectrum of rando m matrices and two-point quantitative invertibility","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2504.15992","last_updated":"2025-04-22T15:54:32Z","snapshot_observed_at":"2026-08-18T22:56:04.352071Z","submitted_at":"2025-04-22T15:54:32Z","title":"Repeated singular values of a random symmetric matrix and decoupled singular value estimates","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-16T11:18:35.688380Z"},"links":{"cited_paper":"/paper/2502.13819","citing_paper":"/paper/2504.15992"},"observation_digest":"sha256:10dc7fcd8635de5c63cbe09fa40c38dc2e66460fc04aeb1d71a7a5a57800f28e","observation_id":"456755b6-cda0-43b9-abf9-e5ce0e4efe21","resolution":{"observed_at":"2026-08-16T11:18:35.688380Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2405.04999","last_updated":"2024-05-14T15:47:51Z","snapshot_observed_at":"2026-08-16T13:54:22.418376Z","submitted_at":"2024-05-08T12:11:10Z","title":"Small ball probability for multiple singular values of symmetric random matrices","version":2},"cited_work":{"arxiv_id":"2405.04999","doi":null,"metadata_source":"pith","pith_arxiv_id":"2405.04999","snapshot_observed_at":"2026-08-16T11:18:35.978529Z","title":"Small ball probability for multiple singular values of symmetric random matrices","venue":"math.PR","work_id":"e722e9f8-db57-4ddb-af2c-32bf38b584a1","year":2024},"citing_paper":{"arxiv_id":"2504.15992","last_updated":"2025-04-22T15:54:32Z","snapshot_observed_at":"2026-08-18T22:56:04.352071Z","submitted_at":"2025-04-22T15:54:32Z","title":"Repeated singular values of a random symmetric matrix and decoupled singular value estimates","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-16T11:18:35.691977Z"},"links":{"cited_paper":"/paper/2405.04999","citing_paper":"/paper/2504.15992"},"observation_digest":"sha256:1a3cc63c53ae67800acc728dded69f8a137caf10f48277c9e9bd9982a3f0947c","observation_id":"7b94bbbe-86ca-41e1-8a9e-d84a4ddd9e1a","resolution":{"observed_at":"2026-08-16T11:18:35.985654Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:18:37.172160Z","title":"A bound on tail probabilit ies for quadratic forms in independent random variables","venue":null,"work_id":"02a7d8f3-811f-4a81-a613-d9a70b4f0373","year":1971},"citing_paper":{"arxiv_id":"2504.15992","last_updated":"2025-04-22T15:54:32Z","snapshot_observed_at":"2026-08-18T22:56:04.352071Z","submitted_at":"2025-04-22T15:54:32Z","title":"Repeated singular values of a random symmetric matrix and decoupled singular value estimates","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-16T11:18:35.696001Z"},"links":{"citing_paper":"/paper/2504.15992"},"observation_digest":"sha256:849709421732d62e7a1b8f621b23b68c8647ad282ac9f4a029149a49fec14bea","observation_id":"9e10a51c-0f87-4449-998f-4f920c70588f","resolution":{"observed_at":"2026-08-16T11:18:37.175862Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:18:36.943898Z","title":"On the s mallest singular value of symmetric random matrices","venue":null,"work_id":"aa234e2c-158c-4af4-91ac-a6e4e4d482da","year":2022},"citing_paper":{"arxiv_id":"2504.15992","last_updated":"2025-04-22T15:54:32Z","snapshot_observed_at":"2026-08-18T22:56:04.352071Z","submitted_at":"2025-04-22T15:54:32Z","title":"Repeated singular values of a random symmetric matrix and decoupled singular value estimates","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-16T11:18:35.700266Z"},"links":{"citing_paper":"/paper/2504.15992"},"observation_digest":"sha256:833e15619cffe0ee4f6e1a5aff910bd5c1dba31bdd88477da36b265141c993a3","observation_id":"1b38f41e-221d-4d7d-9330-d4babdd2b7a5","resolution":{"observed_at":"2026-08-16T11:18:37.075863Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:18:36.688137Z","title":"The smallest singular value of heav y-tailed not necessarily iid random matrices via random rounding","venue":null,"work_id":"f957a9be-9b5c-4418-832a-88d5404b6af0","year":2021},"citing_paper":{"arxiv_id":"2504.15992","last_updated":"2025-04-22T15:54:32Z","snapshot_observed_at":"2026-08-18T22:56:04.352071Z","submitted_at":"2025-04-22T15:54:32Z","title":"Repeated singular values of a random symmetric matrix and decoupled singular value estimates","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-16T11:18:35.704320Z"},"links":{"citing_paper":"/paper/2504.15992"},"observation_digest":"sha256:532e48e3154ba7e7120562b60a3387aa25ed893b1acafe1a39afe036a53a3320","observation_id":"a818534e-679d-4dd5-9125-e0923635c0ae","resolution":{"observed_at":"2026-08-16T11:18:36.815824Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:18:36.678131Z","title":"Tail bounds for gaps betw een eigenvalues of sparse random matrices","venue":null,"work_id":"968e7b52-63bb-4eaf-adb2-ce40d0166f8f","year":2021},"citing_paper":{"arxiv_id":"2504.15992","last_updated":"2025-04-22T15:54:32Z","snapshot_observed_at":"2026-08-18T22:56:04.352071Z","submitted_at":"2025-04-22T15:54:32Z","title":"Repeated singular values of a random symmetric matrix and decoupled singular value estimates","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-16T11:18:35.708498Z"},"links":{"citing_paper":"/paper/2504.15992"},"observation_digest":"sha256:cf68addce088073e02009032fcefecc6c992bf85866f43ea49d6e1e64dd465e3","observation_id":"dab131d8-c930-46f6-b97a-de7b5dd82e3c","resolution":{"observed_at":"2026-08-16T11:18:36.681829Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:18:36.668226Z","title":"Sparse random matrices have simple spectrum","venue":null,"work_id":"83a5a39f-facf-45c5-b066-671a14e75bda","year":2020},"citing_paper":{"arxiv_id":"2504.15992","last_updated":"2025-04-22T15:54:32Z","snapshot_observed_at":"2026-08-18T22:56:04.352071Z","submitted_at":"2025-04-22T15:54:32Z","title":"Repeated singular values of a random symmetric matrix and decoupled singular value estimates","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-16T11:18:35.711797Z"},"links":{"citing_paper":"/paper/2504.15992"},"observation_digest":"sha256:5d6f24f7f1d3776c3f89078b1c40d47fea6717abf4f298b3e38aa7c0c8cc8cc0","observation_id":"9b06fbfd-a352-4ad3-bfac-853a5c7ab15a","resolution":{"observed_at":"2026-08-16T11:18:36.671638Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:18:36.656953Z","title":"Random matrices: t ail bounds for gaps be- tween eigenvalues","venue":null,"work_id":"1945f5ea-a45f-45f9-a65f-b2ac8fecc8e6","year":2017},"citing_paper":{"arxiv_id":"2504.15992","last_updated":"2025-04-22T15:54:32Z","snapshot_observed_at":"2026-08-18T22:56:04.352071Z","submitted_at":"2025-04-22T15:54:32Z","title":"Repeated singular values of a random symmetric matrix and decoupled singular value estimates","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-16T11:18:35.714964Z"},"links":{"citing_paper":"/paper/2504.15992"},"observation_digest":"sha256:b294d1d9ed7ecbbec7926caf238de5b966f8f951daf9063beedc2a19d3c464d2","observation_id":"04a56a1e-9eef-4ea8-8585-1a0fa95e7d59","resolution":{"observed_at":"2026-08-16T11:18:36.660542Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:18:35.718165Z","title":"Inverse Littlewood-Offord problems and t he singularity of ran- dom symmetric matrices","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2504.15992","last_updated":"2025-04-22T15:54:32Z","snapshot_observed_at":"2026-08-18T22:56:04.352071Z","submitted_at":"2025-04-22T15:54:32Z","title":"Repeated singular values of a random symmetric matrix and decoupled singular value estimates","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-16T11:18:35.718165Z"},"links":{"citing_paper":"/paper/2504.15992"},"observation_digest":"sha256:319bde6603b0fadb3099e66ef4ade013effec4ff90584363ebdd5b78e257b5b7","observation_id":"57d5940a-f909-408a-87df-cacf3130b451","resolution":{"observed_at":"2026-08-16T11:18:35.718165Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:18:35.722461Z","title":"No-gaps delocaliz ation for general random matrices","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2504.15992","last_updated":"2025-04-22T15:54:32Z","snapshot_observed_at":"2026-08-18T22:56:04.352071Z","submitted_at":"2025-04-22T15:54:32Z","title":"Repeated singular values of a random symmetric matrix and decoupled singular value estimates","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-16T11:18:35.722461Z"},"links":{"citing_paper":"/paper/2504.15992"},"observation_digest":"sha256:f6e418050a674748fc33bb213a3d0eb2ddb27dfb2cee8eea75a0648659b8a237","observation_id":"35e86928-3a9d-4300-8454-6a592595213f","resolution":{"observed_at":"2026-08-16T11:18:35.722461Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:18:35.725941Z","title":"Smallest singular value of a random rect- angular matrix","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2504.15992","last_updated":"2025-04-22T15:54:32Z","snapshot_observed_at":"2026-08-18T22:56:04.352071Z","submitted_at":"2025-04-22T15:54:32Z","title":"Repeated singular values of a random symmetric matrix and decoupled singular value estimates","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-16T11:18:35.725941Z"},"links":{"citing_paper":"/paper/2504.15992"},"observation_digest":"sha256:0aec9949ccffbe8f2f21087fd352a35d126ceb59080d0688b17420a26d0b0d4f","observation_id":"5db0f931-ca1c-4968-b707-a78358a769d0","resolution":{"observed_at":"2026-08-16T11:18:35.725941Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:18:35.729325Z","title":"The Littlewood–Offo rd problem and invert- ibility of random matrices","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2504.15992","last_updated":"2025-04-22T15:54:32Z","snapshot_observed_at":"2026-08-18T22:56:04.352071Z","submitted_at":"2025-04-22T15:54:32Z","title":"Repeated singular values of a random symmetric matrix and decoupled singular value estimates","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-16T11:18:35.729325Z"},"links":{"citing_paper":"/paper/2504.15992"},"observation_digest":"sha256:4db7b70a6fb593ba8860d5741d7ee1ba385a2f252b29e23303e29534a905476a","observation_id":"e118e1aa-87fb-4548-9376-d6dd97aac979","resolution":{"observed_at":"2026-08-16T11:18:35.729325Z","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":"2026-08-16T11:18:36.622219Z","title":"Random matrices have simple spe ctrum","venue":null,"work_id":"bcd87d99-b12d-4639-b5cb-4896d831d9fe","year":2017},"citing_paper":{"arxiv_id":"2504.15992","last_updated":"2025-04-22T15:54:32Z","snapshot_observed_at":"2026-08-18T22:56:04.352071Z","submitted_at":"2025-04-22T15:54:32Z","title":"Repeated singular values of a random symmetric matrix and decoupled singular value estimates","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-16T11:18:35.732489Z"},"links":{"citing_paper":"/paper/2504.15992"},"observation_digest":"sha256:ce800b879b029267721d3d9c7d93a126e1149d35f6363825f3a05b1a8b6ab2a5","observation_id":"0a9f1ade-71cf-4587-b174-115f484245bc","resolution":{"observed_at":"2026-08-16T11:18:36.626336Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:18:36.380874Z","title":"Random matrices: Universality of local eigenvalue statistics up to the edge","venue":null,"work_id":"fd2d9df6-fb9b-415f-80cf-889b30a7d4b8","year":2010},"citing_paper":{"arxiv_id":"2504.15992","last_updated":"2025-04-22T15:54:32Z","snapshot_observed_at":"2026-08-18T22:56:04.352071Z","submitted_at":"2025-04-22T15:54:32Z","title":"Repeated singular values of a random symmetric matrix and decoupled singular value estimates","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-16T11:18:35.735669Z"},"links":{"citing_paper":"/paper/2504.15992"},"observation_digest":"sha256:81443a6c892e2580c1e4add137659ec20cf7d24ded2d72201a03bf806385acd1","observation_id":"e586d697-38b6-48a1-8792-e612b80b4e24","resolution":{"observed_at":"2026-08-16T11:18:36.495211Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:18:35.775193Z","title":"Singularity of random Bernou lli matrices","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2504.15992","last_updated":"2025-04-22T15:54:32Z","snapshot_observed_at":"2026-08-18T22:56:04.352071Z","submitted_at":"2025-04-22T15:54:32Z","title":"Repeated singular values of a random symmetric matrix and decoupled singular value estimates","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-16T11:18:35.775193Z"},"links":{"citing_paper":"/paper/2504.15992"},"observation_digest":"sha256:fb83296811425ad96510a0f9eece194001c8f6a3c8922e0ee8019e31f965d2f0","observation_id":"1d1f50f8-f908-4fbc-8613-0fa51cbb7160","resolution":{"observed_at":"2026-08-16T11:18:35.775193Z","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":"2026-08-16T11:18:36.364023Z","title":"High-dimensional probability","venue":null,"work_id":"f9a7eb93-8f64-420f-bc86-768fcdbb8670","year":2018},"citing_paper":{"arxiv_id":"2504.15992","last_updated":"2025-04-22T15:54:32Z","snapshot_observed_at":"2026-08-18T22:56:04.352071Z","submitted_at":"2025-04-22T15:54:32Z","title":"Repeated singular values of a random symmetric matrix and decoupled singular value estimates","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-16T11:18:35.846566Z"},"links":{"citing_paper":"/paper/2504.15992"},"observation_digest":"sha256:e95d401f6efa203ee080d65c378c08a799a344ae11b600e4f4da5d19b5f1f4db","observation_id":"1305582c-a335-4e34-9376-1d8d447aac88","resolution":{"observed_at":"2026-08-16T11:18:36.367438Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:18:36.351413Z","title":"Invertibility of symmetric random m atrices","venue":null,"work_id":"52e7f87e-c38b-4bef-87cf-0e3fb033c000","year":2014},"citing_paper":{"arxiv_id":"2504.15992","last_updated":"2025-04-22T15:54:32Z","snapshot_observed_at":"2026-08-18T22:56:04.352071Z","submitted_at":"2025-04-22T15:54:32Z","title":"Repeated singular values of a random symmetric matrix and decoupled singular value estimates","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-16T11:18:35.918211Z"},"links":{"citing_paper":"/paper/2504.15992"},"observation_digest":"sha256:9603de0b54be5b9309af6adc00f06ab1b1c98e24cf8612b073ed4b9a8bf59022","observation_id":"95a62aaf-5d59-4d36-abf1-cbb5fbe9c5d3","resolution":{"observed_at":"2026-08-16T11:18:36.356124Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:18:36.339604Z","title":"Recent progress in combinatorial random mat rix theory","venue":null,"work_id":"5e5f47b3-6236-44a0-a734-9e560b616a2a","year":2021},"citing_paper":{"arxiv_id":"2504.15992","last_updated":"2025-04-22T15:54:32Z","snapshot_observed_at":"2026-08-18T22:56:04.352071Z","submitted_at":"2025-04-22T15:54:32Z","title":"Repeated singular values of a random symmetric matrix and decoupled singular value estimates","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-16T11:18:35.939666Z"},"links":{"citing_paper":"/paper/2504.15992"},"observation_digest":"sha256:1b36037b1541dc0341faf1de65cf65073b1fb952a5f128eddbf683fe51aa1432","observation_id":"506bd9db-2922-4049-9279-fb7fa49a0d75","resolution":{"observed_at":"2026-08-16T11:18:36.343815Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:18:36.328853Z","title":"On the distribution of the roots of cer tain symmetric matrices","venue":null,"work_id":"960c7979-be5a-49e8-89d9-1213289b85a4","year":1958},"citing_paper":{"arxiv_id":"2504.15992","last_updated":"2025-04-22T15:54:32Z","snapshot_observed_at":"2026-08-18T22:56:04.352071Z","submitted_at":"2025-04-22T15:54:32Z","title":"Repeated singular values of a random symmetric matrix and decoupled singular value estimates","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-16T11:18:35.943260Z"},"links":{"citing_paper":"/paper/2504.15992"},"observation_digest":"sha256:02737b8a004ac3be984c118f64922198d5957e6b5bd23ef0cb7dbae7c52bc568","observation_id":"27734194-8ffa-4610-8b15-002853e81ef7","resolution":{"observed_at":"2026-08-16T11:18:36.332539Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:18:36.132085Z","title":"A bound on tail probabilities for quadrat ic forms in independent ran- dom variables whose distributions are not necessarily symm etric","venue":null,"work_id":"b71dca0f-041a-4995-b77f-d281181d8bca","year":1973},"citing_paper":{"arxiv_id":"2504.15992","last_updated":"2025-04-22T15:54:32Z","snapshot_observed_at":"2026-08-18T22:56:04.352071Z","submitted_at":"2025-04-22T15:54:32Z","title":"Repeated singular values of a random symmetric matrix and decoupled singular value estimates","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-16T11:18:35.950200Z"},"links":{"citing_paper":"/paper/2504.15992"},"observation_digest":"sha256:84a0390ae60fb733e90d0463d23cb729523f4480e3d90ad4e57017102a6275be","observation_id":"d6a31a70-da85-42b0-8cbb-68d753800c27","resolution":{"observed_at":"2026-08-16T11:18:36.200942Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2504.15992","last_updated":"2025-04-22T15:54:32Z","latest_version":1,"primary_category":"math.PR","snapshot_observed_at":"2026-08-18T22:56:04.352071Z","submitted_at":"2025-04-22T15:54:32Z","title":"Repeated singular values of a random symmetric matrix and decoupled singular value estimates"},"reference_resolution":{"displayed":37,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":15,"verified_exact":1,"verified_fuzzy":21},"total_outbound_references":37},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"thesis":"As of 20 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 2 inbound Pith citation observations for arXiv:2504.15992."}