{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:MXTG4A5344XUUW5MLBZIEE5OTX","short_pith_number":"pith:MXTG4A53","canonical_record":{"source":{"id":"1206.2251","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-11T15:18:58Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"1e4b2a30eb21756e151372bc1e7af3dc0556f7399a0546b8c2ba0b2458105cdb","abstract_canon_sha256":"772bb4fc4e4013a1e5405c60e06d0bb974ce865ce8f6a0cb47f3d475e3d53d90"},"schema_version":"1.0"},"canonical_sha256":"65e66e03bbe72f4a5bac58728213ae9dffc9365970c93c8169e0bab0b37fd5a3","source":{"kind":"arxiv","id":"1206.2251","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.2251","created_at":"2026-05-18T02:29:32Z"},{"alias_kind":"arxiv_version","alias_value":"1206.2251v2","created_at":"2026-05-18T02:29:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.2251","created_at":"2026-05-18T02:29:32Z"},{"alias_kind":"pith_short_12","alias_value":"MXTG4A5344XU","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MXTG4A5344XUUW5M","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MXTG4A53","created_at":"2026-05-18T12:27:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:MXTG4A5344XUUW5MLBZIEE5OTX","target":"record","payload":{"canonical_record":{"source":{"id":"1206.2251","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-11T15:18:58Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"1e4b2a30eb21756e151372bc1e7af3dc0556f7399a0546b8c2ba0b2458105cdb","abstract_canon_sha256":"772bb4fc4e4013a1e5405c60e06d0bb974ce865ce8f6a0cb47f3d475e3d53d90"},"schema_version":"1.0"},"canonical_sha256":"65e66e03bbe72f4a5bac58728213ae9dffc9365970c93c8169e0bab0b37fd5a3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:32.607058Z","signature_b64":"T8c9O3yxXYNjeFeVFKHeDA2WYUSJsBi+y1fByGMgsxlav8dHV+tKOhML2XQMSq4Gdnvf1+eGXIOSo+ae6sJmBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65e66e03bbe72f4a5bac58728213ae9dffc9365970c93c8169e0bab0b37fd5a3","last_reissued_at":"2026-05-18T02:29:32.606632Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:32.606632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.2251","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:29:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rjwN9A+SDE1SwXTJxUfd78UAugyKnR/hmJrNbGPqVX1aGzwTdbpMe9hUG0Hn00Wf6g1OIbFxG78MHKyHgdvoDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T12:38:25.479503Z"},"content_sha256":"d9d83dd98bb2742424b3ffcc50a27659474d14eee31b569642816cb8b3c23165","schema_version":"1.0","event_id":"sha256:d9d83dd98bb2742424b3ffcc50a27659474d14eee31b569642816cb8b3c23165"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:MXTG4A5344XUUW5MLBZIEE5OTX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Necessary and Sufficient Condition for Edge Universality of Wigner matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Ji Oon Lee, Jun Yin","submitted_at":"2012-06-11T15:18:58Z","abstract_excerpt":"In this paper, we prove a necessary and sufficient condition for Tracy-Widom law of Wigner matrices. Consider $N \\times N$ symmetric Wigner matrices $H$ with $H_{ij} = N^{-1/2} x_{ij}$, whose upper right entries $x_{ij}$ $(1\\le i< j\\le N)$ are $i.i.d.$ random variables with distribution $\\mu$ and diagonal entries $x_{ii}$ $(1\\le i\\le N)$ are $i.i.d.$ random variables with distribution $\\wt \\mu$. The means of $\\mu$ and $\\wt \\mu$ are zero, the variance of $\\mu$ is 1, and the variance of $\\wt \\mu $ is finite. We prove that Tracy-Widom law holds if and only if $\\lim_{s\\to \\infty}s^4\\p(|x_{12}| \\ge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.2251","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:29:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Cipo7NiiBZbL9ITJ7CRhpyLNwoXnanTBRh7akSu+fBepjlj1Uf1AENkGBpkCLJL7+c5LLV9VIR3hPe341RFoDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T12:38:25.480096Z"},"content_sha256":"62ce54a32c776a0e613074742d447777737732b35e0a12053ea12c6144f1a47f","schema_version":"1.0","event_id":"sha256:62ce54a32c776a0e613074742d447777737732b35e0a12053ea12c6144f1a47f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MXTG4A5344XUUW5MLBZIEE5OTX/bundle.json","state_url":"https://pith.science/pith/MXTG4A5344XUUW5MLBZIEE5OTX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MXTG4A5344XUUW5MLBZIEE5OTX/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-26T12:38:25Z","links":{"resolver":"https://pith.science/pith/MXTG4A5344XUUW5MLBZIEE5OTX","bundle":"https://pith.science/pith/MXTG4A5344XUUW5MLBZIEE5OTX/bundle.json","state":"https://pith.science/pith/MXTG4A5344XUUW5MLBZIEE5OTX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MXTG4A5344XUUW5MLBZIEE5OTX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:MXTG4A5344XUUW5MLBZIEE5OTX","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":"772bb4fc4e4013a1e5405c60e06d0bb974ce865ce8f6a0cb47f3d475e3d53d90","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-11T15:18:58Z","title_canon_sha256":"1e4b2a30eb21756e151372bc1e7af3dc0556f7399a0546b8c2ba0b2458105cdb"},"schema_version":"1.0","source":{"id":"1206.2251","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.2251","created_at":"2026-05-18T02:29:32Z"},{"alias_kind":"arxiv_version","alias_value":"1206.2251v2","created_at":"2026-05-18T02:29:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.2251","created_at":"2026-05-18T02:29:32Z"},{"alias_kind":"pith_short_12","alias_value":"MXTG4A5344XU","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MXTG4A5344XUUW5M","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MXTG4A53","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:62ce54a32c776a0e613074742d447777737732b35e0a12053ea12c6144f1a47f","target":"graph","created_at":"2026-05-18T02:29:32Z","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":"In this paper, we prove a necessary and sufficient condition for Tracy-Widom law of Wigner matrices. Consider $N \\times N$ symmetric Wigner matrices $H$ with $H_{ij} = N^{-1/2} x_{ij}$, whose upper right entries $x_{ij}$ $(1\\le i< j\\le N)$ are $i.i.d.$ random variables with distribution $\\mu$ and diagonal entries $x_{ii}$ $(1\\le i\\le N)$ are $i.i.d.$ random variables with distribution $\\wt \\mu$. The means of $\\mu$ and $\\wt \\mu$ are zero, the variance of $\\mu$ is 1, and the variance of $\\wt \\mu $ is finite. We prove that Tracy-Widom law holds if and only if $\\lim_{s\\to \\infty}s^4\\p(|x_{12}| \\ge","authors_text":"Ji Oon Lee, Jun Yin","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-11T15:18:58Z","title":"A Necessary and Sufficient Condition for Edge Universality of Wigner matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.2251","kind":"arxiv","version":2},"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:d9d83dd98bb2742424b3ffcc50a27659474d14eee31b569642816cb8b3c23165","target":"record","created_at":"2026-05-18T02:29:32Z","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":"772bb4fc4e4013a1e5405c60e06d0bb974ce865ce8f6a0cb47f3d475e3d53d90","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-11T15:18:58Z","title_canon_sha256":"1e4b2a30eb21756e151372bc1e7af3dc0556f7399a0546b8c2ba0b2458105cdb"},"schema_version":"1.0","source":{"id":"1206.2251","kind":"arxiv","version":2}},"canonical_sha256":"65e66e03bbe72f4a5bac58728213ae9dffc9365970c93c8169e0bab0b37fd5a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65e66e03bbe72f4a5bac58728213ae9dffc9365970c93c8169e0bab0b37fd5a3","first_computed_at":"2026-05-18T02:29:32.606632Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:32.606632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T8c9O3yxXYNjeFeVFKHeDA2WYUSJsBi+y1fByGMgsxlav8dHV+tKOhML2XQMSq4Gdnvf1+eGXIOSo+ae6sJmBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:32.607058Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.2251","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9d83dd98bb2742424b3ffcc50a27659474d14eee31b569642816cb8b3c23165","sha256:62ce54a32c776a0e613074742d447777737732b35e0a12053ea12c6144f1a47f"],"state_sha256":"a82f7283db6500f21e5395fd11d4ba9197c8ee779f94a2bb59ac6308572b7ce6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7Ie+H0L53dxqL0uq1jSt7VNKj/WorYyqIs4qmyWo2XQ1IiRaRCL0KvdE7kk+JIW3PtjVMH6ACBsajIsaOdP9CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T12:38:25.483133Z","bundle_sha256":"b0d9c4147c94741dfbccf4ce9b5309af06866d2e9954422b8e39c2f93805b3be"}}