{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:U2HLP73VLI5FQRSDLMTBBIC4HC","short_pith_number":"pith:U2HLP73V","canonical_record":{"source":{"id":"1103.5922","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-03-30T13:31:14Z","cross_cats_sorted":["math.CV","math.MP","math.PR"],"title_canon_sha256":"578f489809b72f150b58cd1dcfa82d1a033d549c5d8054f294d887e2cec5e70d","abstract_canon_sha256":"6a633655670ba449edd3ad84c0d995901eef0fb7252213e444385ea70790c2c9"},"schema_version":"1.0"},"canonical_sha256":"a68eb7ff755a3a5846435b2610a05c3889bdff9b3262bdfea9dd8872ffd4888d","source":{"kind":"arxiv","id":"1103.5922","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.5922","created_at":"2026-05-18T02:29:16Z"},{"alias_kind":"arxiv_version","alias_value":"1103.5922v2","created_at":"2026-05-18T02:29:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.5922","created_at":"2026-05-18T02:29:16Z"},{"alias_kind":"pith_short_12","alias_value":"U2HLP73VLI5F","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"U2HLP73VLI5FQRSD","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"U2HLP73V","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:U2HLP73VLI5FQRSDLMTBBIC4HC","target":"record","payload":{"canonical_record":{"source":{"id":"1103.5922","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-03-30T13:31:14Z","cross_cats_sorted":["math.CV","math.MP","math.PR"],"title_canon_sha256":"578f489809b72f150b58cd1dcfa82d1a033d549c5d8054f294d887e2cec5e70d","abstract_canon_sha256":"6a633655670ba449edd3ad84c0d995901eef0fb7252213e444385ea70790c2c9"},"schema_version":"1.0"},"canonical_sha256":"a68eb7ff755a3a5846435b2610a05c3889bdff9b3262bdfea9dd8872ffd4888d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:16.250792Z","signature_b64":"PFLzWv0Z+nD2ADBbcC5q+EjUDVsFm5RH2KtHaXR/v1MzTIXZZVkPd9oY5MifZh22kSYc8dCI7IjYbnvfSAlVAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a68eb7ff755a3a5846435b2610a05c3889bdff9b3262bdfea9dd8872ffd4888d","last_reissued_at":"2026-05-18T02:29:16.250374Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:16.250374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.5922","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":"2026-05-18T02:29:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q3zFhiXrj+lhkyx0Why6fJi0ANJcyydhiqP1kc0HOQxrwJFAOIkGcYypoBcus+xGA2yyOqQF/xuVM0XybDwBBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T18:15:19.709529Z"},"content_sha256":"fcd5ccfe7e6dd5272c0aa14ffe35d61c5551faa7e3c27dcf06712e5dc00b49ac","schema_version":"1.0","event_id":"sha256:fcd5ccfe7e6dd5272c0aa14ffe35d61c5551faa7e3c27dcf06712e5dc00b49ac"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:U2HLP73VLI5FQRSDLMTBBIC4HC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Universality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"A.B.J. Kuijlaars","submitted_at":"2011-03-30T13:31:14Z","abstract_excerpt":"Universality of eigenvalue spacings is one of the basic characteristics of random matrices. We give the precise meaning of universality and discuss the standard universality classes (sine, Airy, Bessel) and their appearance in unitary, orthogonal, and symplectic ensembles. The Riemann-Hilbert problem for orthogonal polynomials is one possible tool to derive universality in unitary random matrix ensembles. An overview is presented of the Deift/Zhou steepest descent analysis of the Riemann-Hilbert problem in the one-cut regular case. Non-standard universality classes that arise at singular point"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.5922","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":"2026-05-18T02:29:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uXDUdFRvAP5kCw9k/TNigUz3RIj1XoKc5jDgQ1j3lY6XZmRYOMdAKJTUeKX1H3kxe/oy4s+tuZnsQXYq1aK4DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T18:15:19.710305Z"},"content_sha256":"8030aae94fc97a58b9621934c99e6e7beedbcdd34625e9e8d24fe467ea337fea","schema_version":"1.0","event_id":"sha256:8030aae94fc97a58b9621934c99e6e7beedbcdd34625e9e8d24fe467ea337fea"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U2HLP73VLI5FQRSDLMTBBIC4HC/bundle.json","state_url":"https://pith.science/pith/U2HLP73VLI5FQRSDLMTBBIC4HC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U2HLP73VLI5FQRSDLMTBBIC4HC/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":"2026-05-31T18:15:19Z","links":{"resolver":"https://pith.science/pith/U2HLP73VLI5FQRSDLMTBBIC4HC","bundle":"https://pith.science/pith/U2HLP73VLI5FQRSDLMTBBIC4HC/bundle.json","state":"https://pith.science/pith/U2HLP73VLI5FQRSDLMTBBIC4HC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U2HLP73VLI5FQRSDLMTBBIC4HC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:U2HLP73VLI5FQRSDLMTBBIC4HC","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":"6a633655670ba449edd3ad84c0d995901eef0fb7252213e444385ea70790c2c9","cross_cats_sorted":["math.CV","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-03-30T13:31:14Z","title_canon_sha256":"578f489809b72f150b58cd1dcfa82d1a033d549c5d8054f294d887e2cec5e70d"},"schema_version":"1.0","source":{"id":"1103.5922","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.5922","created_at":"2026-05-18T02:29:16Z"},{"alias_kind":"arxiv_version","alias_value":"1103.5922v2","created_at":"2026-05-18T02:29:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.5922","created_at":"2026-05-18T02:29:16Z"},{"alias_kind":"pith_short_12","alias_value":"U2HLP73VLI5F","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"U2HLP73VLI5FQRSD","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"U2HLP73V","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:8030aae94fc97a58b9621934c99e6e7beedbcdd34625e9e8d24fe467ea337fea","target":"graph","created_at":"2026-05-18T02:29:16Z","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":"Universality of eigenvalue spacings is one of the basic characteristics of random matrices. We give the precise meaning of universality and discuss the standard universality classes (sine, Airy, Bessel) and their appearance in unitary, orthogonal, and symplectic ensembles. The Riemann-Hilbert problem for orthogonal polynomials is one possible tool to derive universality in unitary random matrix ensembles. An overview is presented of the Deift/Zhou steepest descent analysis of the Riemann-Hilbert problem in the one-cut regular case. Non-standard universality classes that arise at singular point","authors_text":"A.B.J. Kuijlaars","cross_cats":["math.CV","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-03-30T13:31:14Z","title":"Universality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.5922","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:fcd5ccfe7e6dd5272c0aa14ffe35d61c5551faa7e3c27dcf06712e5dc00b49ac","target":"record","created_at":"2026-05-18T02:29:16Z","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":"6a633655670ba449edd3ad84c0d995901eef0fb7252213e444385ea70790c2c9","cross_cats_sorted":["math.CV","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-03-30T13:31:14Z","title_canon_sha256":"578f489809b72f150b58cd1dcfa82d1a033d549c5d8054f294d887e2cec5e70d"},"schema_version":"1.0","source":{"id":"1103.5922","kind":"arxiv","version":2}},"canonical_sha256":"a68eb7ff755a3a5846435b2610a05c3889bdff9b3262bdfea9dd8872ffd4888d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a68eb7ff755a3a5846435b2610a05c3889bdff9b3262bdfea9dd8872ffd4888d","first_computed_at":"2026-05-18T02:29:16.250374Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:16.250374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PFLzWv0Z+nD2ADBbcC5q+EjUDVsFm5RH2KtHaXR/v1MzTIXZZVkPd9oY5MifZh22kSYc8dCI7IjYbnvfSAlVAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:16.250792Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.5922","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fcd5ccfe7e6dd5272c0aa14ffe35d61c5551faa7e3c27dcf06712e5dc00b49ac","sha256:8030aae94fc97a58b9621934c99e6e7beedbcdd34625e9e8d24fe467ea337fea"],"state_sha256":"543ea0f36425a8a5e0bfd2d62c6a6473cd84fc4f60763ac2f9a519865ae2d07b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ytxK2JrO8ndEsLZn1qgWNC2vn4qwdpRHm18vUGtiizpKdK+bNGWKB/kdlPLdvKQeU/W2T8S1niOR6JZOoBCADg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T18:15:19.714640Z","bundle_sha256":"c9210e491d5e75db33bcd779a7908dcf7a42a0423badabcd32c01b07f308ad34"}}