{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:SC7DKIXEE3FKFA6DNN4XVVMVHY","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":"d53ab6e37eb840db088d971d75359581d593628f710c49f5367f82db2b8f3143","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-03-07T20:44:24Z","title_canon_sha256":"162060a11ea75103c3b46d2902b9e5849cadd50676c67df4a7248ce0e0c22abc"},"schema_version":"1.0","source":{"id":"1203.1605","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.1605","created_at":"2026-05-18T03:46:45Z"},{"alias_kind":"arxiv_version","alias_value":"1203.1605v3","created_at":"2026-05-18T03:46:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.1605","created_at":"2026-05-18T03:46:45Z"},{"alias_kind":"pith_short_12","alias_value":"SC7DKIXEE3FK","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"SC7DKIXEE3FKFA6D","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"SC7DKIXE","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:e2f31aabece20c50d13640b375c70e87bed8fcb571cf8ed5d849e2b120d42af8","target":"graph","created_at":"2026-05-18T03:46:45Z","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 show that the distribution of (a suitable rescaling of) a single eigenvalue gap $\\lambda_{i+1}(M_n)-\\lambda_i(M_n)$ of a random Wigner matrix ensemble in the bulk is asymptotically given by the Gaudin-Mehta distribution, if the Wigner ensemble obeys a finite moment condition and matches moments with the GUE ensemble to fourth order. This is new even in the GUE case, as prior results establishing the Gaudin-Mehta law required either an averaging in the eigenvalue index parameter $i$, or fixing the energy level $u$ instead of the eigenvalue index.\n  The extension from the GUE case to the Wign","authors_text":"Terence Tao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-03-07T20:44:24Z","title":"The asymptotic distribution of a single eigenvalue gap of a Wigner matrix"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.1605","kind":"arxiv","version":3},"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":"sha256:24a796651c61ea9c27ef622634b302cff968440e42bda92f304fb5a511d75049","target":"record","created_at":"2026-05-18T03:46:45Z","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":"d53ab6e37eb840db088d971d75359581d593628f710c49f5367f82db2b8f3143","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-03-07T20:44:24Z","title_canon_sha256":"162060a11ea75103c3b46d2902b9e5849cadd50676c67df4a7248ce0e0c22abc"},"schema_version":"1.0","source":{"id":"1203.1605","kind":"arxiv","version":3}},"canonical_sha256":"90be3522e426caa283c36b797ad5953e2f4abe6bfa7a0f09471b24e4f39dc297","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"90be3522e426caa283c36b797ad5953e2f4abe6bfa7a0f09471b24e4f39dc297","first_computed_at":"2026-05-18T03:46:45.252955Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:45.252955Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QfxDs6E1MgTSrzW5+YyQSYh7kvWxRzla7ix2BJbC9jjkPjK1koWjW1yIY3zH/YhCkjmsBdOq0yc1PQhvCYYPCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:45.253635Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.1605","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:24a796651c61ea9c27ef622634b302cff968440e42bda92f304fb5a511d75049","sha256:e2f31aabece20c50d13640b375c70e87bed8fcb571cf8ed5d849e2b120d42af8"],"state_sha256":"9c7430d3d5f2cd083dd40add03b51282bca91d63fbdd892ce31f2ee46acf9260"}