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We will be working in the regime $N/M=d_N,\\lim_{N\\to\\infty}d_N\\neq0,1,\\infty$. In this paper we prove the edge universality of correlation matrices ${X}^{\\dagger}X$, where the rectangular matrix $X$ (called the standardized matrix) is obtained by normalizing each column of the data matrix $\\widetilde{X}$ by it"},"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":"1112.2381","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-12-11T18:27:08Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"95f02994fc9f45ceed5f078bea98894a55eef8a0674b8effeb29735565fd6735","abstract_canon_sha256":"d881ac12ab34cd609786fc6c3b452c367caa4151718275cdfd9382b7b2d3f8f3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:04.626144Z","signature_b64":"+fnmrQ+b3KflA7+wGvQNOJnREoKWTchrk9DIWdVKLQcCpVyYrsB3jhn23bWr8ok8tMYUf6YKp2SXYcH4KLI9Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"20373f1b31678b13e8f1f664b72f80900116dd6d87699d04b4f6089412983776","last_reissued_at":"2026-05-18T03:44:04.625333Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:04.625333Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Edge universality of correlation matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Jun Yin, Natesh S. 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