{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:VGJCXTJ3M6ZN3GZ5BKAFFDVFLA","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"3e72c5e180cf279b0dee3a5b4a8527c55355f0868a57a7c97f531d1d6603fc17","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2009-12-07T20:51:24Z","title_canon_sha256":"660e46b87cf49ec5f5333440b942eba72517ede2ff1c2360e853dc01c69da1cc"},"schema_version":"1.0","source":{"id":"0912.0966","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.0966","created_at":"2026-05-18T03:55:00Z"},{"alias_kind":"arxiv_version","alias_value":"0912.0966v5","created_at":"2026-05-18T03:55:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.0966","created_at":"2026-05-18T03:55:00Z"},{"alias_kind":"pith_short_12","alias_value":"VGJCXTJ3M6ZN","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"VGJCXTJ3M6ZN3GZ5","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"VGJCXTJ3","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:5c430925facd82aa6417905c832a30d0e885f5ba9a098c01b3296b46e74d2e03","target":"graph","created_at":"2026-05-18T03:55:00Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study the eigenvalues of the covariance matrix $\\frac{1}{n}M^*M$ of a large rectangular matrix $M=M_{n,p}=(\\zeta_{ij})_{1\\leq i\\leq p;1\\leq j\\leq n}$ whose entries are i.i.d. random variables of mean zero, variance one, and having finite $C_0$th moment for some sufficiently large constant $C_0$. The main result of this paper is a Four Moment theorem for i.i.d. covariance matrices (analogous to the Four Moment theorem for Wigner matrices established by the authors in [Acta Math. (2011) Random matrices: Universality of local eigenvalue statistics] (see also [Comm. Math. Phys. 298 (2010) 549--","authors_text":"Terence Tao, Van Vu","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2009-12-07T20:51:24Z","title":"Random covariance matrices: Universality of local statistics of eigenvalues"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.0966","kind":"arxiv","version":5},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c6ffeb7f459d16abc1212de549db0f9d0e069827c51e30546e98f273c0bf9eb6","target":"record","created_at":"2026-05-18T03:55:00Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"3e72c5e180cf279b0dee3a5b4a8527c55355f0868a57a7c97f531d1d6603fc17","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2009-12-07T20:51:24Z","title_canon_sha256":"660e46b87cf49ec5f5333440b942eba72517ede2ff1c2360e853dc01c69da1cc"},"schema_version":"1.0","source":{"id":"0912.0966","kind":"arxiv","version":5}},"canonical_sha256":"a9922bcd3b67b2dd9b3d0a80528ea558108740ec87c952de8042e59023b98d9b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a9922bcd3b67b2dd9b3d0a80528ea558108740ec87c952de8042e59023b98d9b","first_computed_at":"2026-05-18T03:55:00.658604Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:55:00.658604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dsiiRedAbBqvfRhs4bo23ggyfG5UuEySmkNmhKcPwOFu2vfIciiIm1ENVMHbNWAsBbFUVHza/smzcvhqHKy6CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:55:00.659308Z","signed_message":"canonical_sha256_bytes"},"source_id":"0912.0966","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c6ffeb7f459d16abc1212de549db0f9d0e069827c51e30546e98f273c0bf9eb6","sha256:5c430925facd82aa6417905c832a30d0e885f5ba9a098c01b3296b46e74d2e03"],"state_sha256":"dd711a44fb39a79ed7fcaa87dca307723d47041e63b334374a7d1d863f1c4f5f"}