{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:R7V2S4DQDLMJPUQQFANLS6MCGJ","short_pith_number":"pith:R7V2S4DQ","canonical_record":{"source":{"id":"1307.6012","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-07-23T10:17:08Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"75fde0b9162525071ca5f45f1bb907a2229b37fbb71981bac7afe2d6544d5189","abstract_canon_sha256":"3200ea23af2effe021991c01a35afaf7d24de52e723ca7408a2e9a96388a69a7"},"schema_version":"1.0"},"canonical_sha256":"8feba970701ad897d210281ab979823278ee92d10aafe7063ca67ea90daeb070","source":{"kind":"arxiv","id":"1307.6012","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.6012","created_at":"2026-05-18T01:48:41Z"},{"alias_kind":"arxiv_version","alias_value":"1307.6012v1","created_at":"2026-05-18T01:48:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.6012","created_at":"2026-05-18T01:48:41Z"},{"alias_kind":"pith_short_12","alias_value":"R7V2S4DQDLMJ","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"R7V2S4DQDLMJPUQQ","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"R7V2S4DQ","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:R7V2S4DQDLMJPUQQFANLS6MCGJ","target":"record","payload":{"canonical_record":{"source":{"id":"1307.6012","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-07-23T10:17:08Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"75fde0b9162525071ca5f45f1bb907a2229b37fbb71981bac7afe2d6544d5189","abstract_canon_sha256":"3200ea23af2effe021991c01a35afaf7d24de52e723ca7408a2e9a96388a69a7"},"schema_version":"1.0"},"canonical_sha256":"8feba970701ad897d210281ab979823278ee92d10aafe7063ca67ea90daeb070","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:48:41.228598Z","signature_b64":"cUEAXh72rMO75mi6EIqi9xHy5OM+Pyo+uQUHtV37N2YN9qdS1q++y02juN8zEjeUZmrY0OaIWXx3LerEfj9YCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8feba970701ad897d210281ab979823278ee92d10aafe7063ca67ea90daeb070","last_reissued_at":"2026-05-18T01:48:41.228091Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:48:41.228091Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.6012","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:48:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eBMYVglR9+MaKe8BuJQ9tiJ8tmsMBB1JnuvjnGKDf7b77uMF4b059aiUzwgPNKg5MJVqMqezaZ/I3Ac+E646Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T01:26:36.390529Z"},"content_sha256":"27e5528a1dfd313adee59a36bf3084f598582ae7385f278b2d22eb98d4697da1","schema_version":"1.0","event_id":"sha256:27e5528a1dfd313adee59a36bf3084f598582ae7385f278b2d22eb98d4697da1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:R7V2S4DQDLMJPUQQFANLS6MCGJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A method for calculating spectral statistics based on random-matrix universality with an application to the three-point correlations of the Riemann zeros","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"E. Bogomolny, J.P. Keating","submitted_at":"2013-07-23T10:17:08Z","abstract_excerpt":"We illustrate a general method for calculating spectral statistics that combines the universal (Random Matrix Theory limit) and the non-universal (trace-formula-related) contributions by giving a heuristic derivation of the three-point correlation function for the zeros of the Riemann zeta function. The main idea is to construct a generalized Hermitian random matrix ensemble whose mean eigenvalue density coincides with a large but finite portion of the actual density of the spectrum or the Riemann zeros. Averaging the random matrix result over remaining oscillatory terms related, in the case o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.6012","kind":"arxiv","version":1},"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":"2026-05-18T01:48:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PLxf8GxcFczUIsvFFLIE4x72xYHuogJiQMPEP9fMx5LU9qp/iXapbjFvyzKQg608k3GC+IpOaa59yG4vjyUOBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T01:26:36.391293Z"},"content_sha256":"79fe423148768491c087415f7d043875408804b739420e790b9c327c7b7d8fd7","schema_version":"1.0","event_id":"sha256:79fe423148768491c087415f7d043875408804b739420e790b9c327c7b7d8fd7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R7V2S4DQDLMJPUQQFANLS6MCGJ/bundle.json","state_url":"https://pith.science/pith/R7V2S4DQDLMJPUQQFANLS6MCGJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R7V2S4DQDLMJPUQQFANLS6MCGJ/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":"2026-06-10T01:26:36Z","links":{"resolver":"https://pith.science/pith/R7V2S4DQDLMJPUQQFANLS6MCGJ","bundle":"https://pith.science/pith/R7V2S4DQDLMJPUQQFANLS6MCGJ/bundle.json","state":"https://pith.science/pith/R7V2S4DQDLMJPUQQFANLS6MCGJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R7V2S4DQDLMJPUQQFANLS6MCGJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:R7V2S4DQDLMJPUQQFANLS6MCGJ","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":"3200ea23af2effe021991c01a35afaf7d24de52e723ca7408a2e9a96388a69a7","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-07-23T10:17:08Z","title_canon_sha256":"75fde0b9162525071ca5f45f1bb907a2229b37fbb71981bac7afe2d6544d5189"},"schema_version":"1.0","source":{"id":"1307.6012","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.6012","created_at":"2026-05-18T01:48:41Z"},{"alias_kind":"arxiv_version","alias_value":"1307.6012v1","created_at":"2026-05-18T01:48:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.6012","created_at":"2026-05-18T01:48:41Z"},{"alias_kind":"pith_short_12","alias_value":"R7V2S4DQDLMJ","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"R7V2S4DQDLMJPUQQ","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"R7V2S4DQ","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:79fe423148768491c087415f7d043875408804b739420e790b9c327c7b7d8fd7","target":"graph","created_at":"2026-05-18T01:48:41Z","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 illustrate a general method for calculating spectral statistics that combines the universal (Random Matrix Theory limit) and the non-universal (trace-formula-related) contributions by giving a heuristic derivation of the three-point correlation function for the zeros of the Riemann zeta function. The main idea is to construct a generalized Hermitian random matrix ensemble whose mean eigenvalue density coincides with a large but finite portion of the actual density of the spectrum or the Riemann zeros. Averaging the random matrix result over remaining oscillatory terms related, in the case o","authors_text":"E. Bogomolny, J.P. Keating","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-07-23T10:17:08Z","title":"A method for calculating spectral statistics based on random-matrix universality with an application to the three-point correlations of the Riemann zeros"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.6012","kind":"arxiv","version":1},"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":"sha256:27e5528a1dfd313adee59a36bf3084f598582ae7385f278b2d22eb98d4697da1","target":"record","created_at":"2026-05-18T01:48:41Z","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":"3200ea23af2effe021991c01a35afaf7d24de52e723ca7408a2e9a96388a69a7","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-07-23T10:17:08Z","title_canon_sha256":"75fde0b9162525071ca5f45f1bb907a2229b37fbb71981bac7afe2d6544d5189"},"schema_version":"1.0","source":{"id":"1307.6012","kind":"arxiv","version":1}},"canonical_sha256":"8feba970701ad897d210281ab979823278ee92d10aafe7063ca67ea90daeb070","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8feba970701ad897d210281ab979823278ee92d10aafe7063ca67ea90daeb070","first_computed_at":"2026-05-18T01:48:41.228091Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:48:41.228091Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cUEAXh72rMO75mi6EIqi9xHy5OM+Pyo+uQUHtV37N2YN9qdS1q++y02juN8zEjeUZmrY0OaIWXx3LerEfj9YCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:48:41.228598Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.6012","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:27e5528a1dfd313adee59a36bf3084f598582ae7385f278b2d22eb98d4697da1","sha256:79fe423148768491c087415f7d043875408804b739420e790b9c327c7b7d8fd7"],"state_sha256":"88dbda6f254133c82a458220eae0418fd648d3790864418c43547a6e0fcd3f24"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5ApIJC9XSZagwIvyjklB4S7TXSleufzJk5o5PGuDmHeAWldtYlU18kdVMPBVTt3O2HuIf1jSPclCeA8RpLHiDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T01:26:36.395611Z","bundle_sha256":"5f236944295e4cdf8c61ba57d245677f32aba37a9e7ffe6216673ac79e2ca91c"}}