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More precisely, \\begin{eqnarray*}\\sup_{x\\in {\\mathbf {R}}}\\biggl|{\\mathbf {P}}\\biggl(\\frac{\\log(|\\det A_n|)-({1}/{2})\\log (n-1)!}{\\sqrt{({1}/{2})\\log n}}\\le x\\biggr)-{\\mathbf {P}}\\bigl(\\mathbf {N}(0,1)\\le x\\bigr)\\biggr|\\\\\\qquad\\le\\log^{-{1}/{3}+o(1)}n.\\end{eqnarray*}"},"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":"1112.0752","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-12-04T13:55:51Z","cross_cats_sorted":[],"title_canon_sha256":"513487d141a6f79dadc8bebbebf4a5efa3ae5e74da809e81d3c29e171954af37","abstract_canon_sha256":"9ebd748f48ccf98de1a9a4b381803acbf0339179235f0d9fe3da11a5f11c9c9e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:44.079846Z","signature_b64":"J0G1eLorVz+SXF/B6FJgLPKBSS4DwRdZukcxX4sXJudxZ3UemKvmeaFL1pah3hFQde7nypcWyXazfOWny/XWCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad1c45bb78b8900515af5c668ab745802f4fa43ac94090dba85092e365d8e47b","last_reissued_at":"2026-05-18T03:02:44.079194Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:44.079194Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Random matrices: Law of the determinant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Hoi H. 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