{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:DHGW2MN3A5FKZJPZFU34ZUNBEG","short_pith_number":"pith:DHGW2MN3","schema_version":"1.0","canonical_sha256":"19cd6d31bb074aaca5f92d37ccd1a121978dcd14f3334919981d767de4c35700","source":{"kind":"arxiv","id":"2606.21137","version":1},"attestation_state":"computed","paper":{"title":"A Sudakov--Fernique proof of Lehner-type edge bounds for matrix-valued GUE sums","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.PR","authors_text":"Benoit Collins, Yuta Yamagishi","submitted_at":"2026-06-19T06:22:37Z","abstract_excerpt":"Let $A_0,A_1,\\ldots,A_n\\in M_N(\\mathbb{C})$ be Hermitian matrices and let $G_1,\\ldots,G_n$ be independent $M\\times M$ GUE matrices normalized so that $\\|M^{-1/2}G_i\\|\\to 2$ almost surely as $M\\to\\infty$. We study the spectral edges and operator norm of $H_M = A_0\\otimes I_M + \\frac{1}{\\sqrt{M}}\\sum_{i=1}^n A_i\\otimes G_i$. Lehner's formula identifies the right and left edges of the corresponding free semicircular operator as $\\rho_+ = \\inf_{Z\\succ 0}\\lambda_{\\max}(A_0+Z+\\sum_{i=1}^n A_iZ^{-1}A_i)$ and $\\rho_- = \\sup_{Z\\prec 0}\\lambda_{\\min}(A_0+Z+\\sum_{i=1}^n A_iZ^{-1}A_i)$. Assuming $A_i\\succ"},"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":"2606.21137","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-06-19T06:22:37Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"f47940ef8c314600b8f15e8470ae4fbbb4907484f3ffd66fae1cc9b847cc3da2","abstract_canon_sha256":"88848797a361786619a736684720cc46437468fe19f23ea156b17ac1e4e2a608"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T01:12:31.069187Z","signature_b64":"yCnq7dJG+34PhjhU1tbtcgXWvltUYKeMPeFPlLROBcCdfskoUIHSc9IqERKufLrXHNY7Fk31fxhZJ3YRrOfvDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19cd6d31bb074aaca5f92d37ccd1a121978dcd14f3334919981d767de4c35700","last_reissued_at":"2026-06-23T01:12:31.068687Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T01:12:31.068687Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Sudakov--Fernique proof of Lehner-type edge bounds for matrix-valued GUE sums","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.PR","authors_text":"Benoit Collins, Yuta Yamagishi","submitted_at":"2026-06-19T06:22:37Z","abstract_excerpt":"Let $A_0,A_1,\\ldots,A_n\\in M_N(\\mathbb{C})$ be Hermitian matrices and let $G_1,\\ldots,G_n$ be independent $M\\times M$ GUE matrices normalized so that $\\|M^{-1/2}G_i\\|\\to 2$ almost surely as $M\\to\\infty$. We study the spectral edges and operator norm of $H_M = A_0\\otimes I_M + \\frac{1}{\\sqrt{M}}\\sum_{i=1}^n A_i\\otimes G_i$. Lehner's formula identifies the right and left edges of the corresponding free semicircular operator as $\\rho_+ = \\inf_{Z\\succ 0}\\lambda_{\\max}(A_0+Z+\\sum_{i=1}^n A_iZ^{-1}A_i)$ and $\\rho_- = \\sup_{Z\\prec 0}\\lambda_{\\min}(A_0+Z+\\sum_{i=1}^n A_iZ^{-1}A_i)$. 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