{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:YWGGIYI6CKUPRTAP3AMDU23BNG","short_pith_number":"pith:YWGGIYI6","schema_version":"1.0","canonical_sha256":"c58c64611e12a8f8cc0fd8183a6b61698f167fcc363be1e5391f455587584634","source":{"kind":"arxiv","id":"1501.07840","version":4},"attestation_state":"computed","paper":{"title":"Local Single Ring Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Florent Benaych-Georges","submitted_at":"2015-01-30T16:57:04Z","abstract_excerpt":"The Single Ring Theorem, by Guionnet, Krishnapur and Zeitouni, describes the empirical eigenvalue distribution of a large generic matrix with prescribed singular values, i.e. an $N\\times N$ matrix of the form $A=UTV$, with $U, V$ some independent Haar-distributed unitary matrices and $T$ a deterministic matrix whose singular values are the ones prescribed. In this text, we give a local version of this result, proving that it remains true at the microscopic scale $(\\log N)^{-1/4}$. On our way to prove it, we prove a matrix subordination result for singular values of sums of non Hermitian matric"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1501.07840","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-30T16:57:04Z","cross_cats_sorted":[],"title_canon_sha256":"b9e550de80ca71ac000c44252493bb6ddfd22205c29de2a27903c94976779699","abstract_canon_sha256":"bc7987d1c647ad703b2a8cd3313248a67a88eb952b5788b3efe5cf6650b81485"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:21.826301Z","signature_b64":"NtoZJCUkqHaniZDidBJMLLlh0yyN2QbvUC55tcXnNDzZY5OvN2C8ggMqD7B4+0pIMAxxuP/TEuP5fX5UoNbZDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c58c64611e12a8f8cc0fd8183a6b61698f167fcc363be1e5391f455587584634","last_reissued_at":"2026-05-18T01:16:21.825667Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:21.825667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local Single Ring Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Florent Benaych-Georges","submitted_at":"2015-01-30T16:57:04Z","abstract_excerpt":"The Single Ring Theorem, by Guionnet, Krishnapur and Zeitouni, describes the empirical eigenvalue distribution of a large generic matrix with prescribed singular values, i.e. an $N\\times N$ matrix of the form $A=UTV$, with $U, V$ some independent Haar-distributed unitary matrices and $T$ a deterministic matrix whose singular values are the ones prescribed. In this text, we give a local version of this result, proving that it remains true at the microscopic scale $(\\log N)^{-1/4}$. On our way to prove it, we prove a matrix subordination result for singular values of sums of non Hermitian matric"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.07840","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1501.07840","created_at":"2026-05-18T01:16:21.825752+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.07840v4","created_at":"2026-05-18T01:16:21.825752+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.07840","created_at":"2026-05-18T01:16:21.825752+00:00"},{"alias_kind":"pith_short_12","alias_value":"YWGGIYI6CKUP","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"YWGGIYI6CKUPRTAP","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"YWGGIYI6","created_at":"2026-05-18T12:29:52.810259+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YWGGIYI6CKUPRTAP3AMDU23BNG","json":"https://pith.science/pith/YWGGIYI6CKUPRTAP3AMDU23BNG.json","graph_json":"https://pith.science/api/pith-number/YWGGIYI6CKUPRTAP3AMDU23BNG/graph.json","events_json":"https://pith.science/api/pith-number/YWGGIYI6CKUPRTAP3AMDU23BNG/events.json","paper":"https://pith.science/paper/YWGGIYI6"},"agent_actions":{"view_html":"https://pith.science/pith/YWGGIYI6CKUPRTAP3AMDU23BNG","download_json":"https://pith.science/pith/YWGGIYI6CKUPRTAP3AMDU23BNG.json","view_paper":"https://pith.science/paper/YWGGIYI6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.07840&json=true","fetch_graph":"https://pith.science/api/pith-number/YWGGIYI6CKUPRTAP3AMDU23BNG/graph.json","fetch_events":"https://pith.science/api/pith-number/YWGGIYI6CKUPRTAP3AMDU23BNG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YWGGIYI6CKUPRTAP3AMDU23BNG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YWGGIYI6CKUPRTAP3AMDU23BNG/action/storage_attestation","attest_author":"https://pith.science/pith/YWGGIYI6CKUPRTAP3AMDU23BNG/action/author_attestation","sign_citation":"https://pith.science/pith/YWGGIYI6CKUPRTAP3AMDU23BNG/action/citation_signature","submit_replication":"https://pith.science/pith/YWGGIYI6CKUPRTAP3AMDU23BNG/action/replication_record"}},"created_at":"2026-05-18T01:16:21.825752+00:00","updated_at":"2026-05-18T01:16:21.825752+00:00"}