{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:GZ5RKNSUF62V3H4EX74FTWNQ5U","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":"a50dd7567e6d473212bfe0b29c427ead11cc443c017cb8273c5d3682d74df120","cross_cats_sorted":["math.CA","math.CV","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-05-22T17:45:57Z","title_canon_sha256":"8b507387b1819c4ae61b8ff2ee9445c6959f0e98dc6725c9f5c25389af6d58df"},"schema_version":"1.0","source":{"id":"1805.08760","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.08760","created_at":"2026-05-17T23:40:04Z"},{"alias_kind":"arxiv_version","alias_value":"1805.08760v5","created_at":"2026-05-17T23:40:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.08760","created_at":"2026-05-17T23:40:04Z"},{"alias_kind":"pith_short_12","alias_value":"GZ5RKNSUF62V","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GZ5RKNSUF62V3H4E","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GZ5RKNSU","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:a20f833bde4573c405fdb3ae1aba22eddaa4c3f2a46aa5fa4011f6392cf9c783","target":"graph","created_at":"2026-05-17T23:40:04Z","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 establish a new connection between moments of $n \\times n$ random matrices $X_n$ and hypergeometric orthogonal polynomials. Specifically, we consider moments $\\mathbb{E}\\mathrm{Tr} X_n^{-s}$ as a function of the complex variable $s \\in \\mathbb{C}$, whose analytic structure we describe completely. We discover several remarkable features, including a reflection symmetry (or functional equation), zeros on a critical line in the complex plane, and orthogonality relations. An application of the theory resolves part of an integrality conjecture of Cunden et al. [F. D. Cunden, F. Mezzadri, N. J. S","authors_text":"Fabio Deelan Cunden, Francesco Mezzadri, Neil O'Connell, Nick Simm","cross_cats":["math.CA","math.CV","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-05-22T17:45:57Z","title":"Moments of random matrices and hypergeometric orthogonal polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.08760","kind":"arxiv","version":5},"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":"sha256:6b687a1c59f07b11a6bd50577f3ea3370dce0680c6471ae09a2a9f16099f9321","target":"record","created_at":"2026-05-17T23:40:04Z","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":"a50dd7567e6d473212bfe0b29c427ead11cc443c017cb8273c5d3682d74df120","cross_cats_sorted":["math.CA","math.CV","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-05-22T17:45:57Z","title_canon_sha256":"8b507387b1819c4ae61b8ff2ee9445c6959f0e98dc6725c9f5c25389af6d58df"},"schema_version":"1.0","source":{"id":"1805.08760","kind":"arxiv","version":5}},"canonical_sha256":"367b1536542fb55d9f84bff859d9b0ed37448e949d5234a92bbbc08780c197eb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"367b1536542fb55d9f84bff859d9b0ed37448e949d5234a92bbbc08780c197eb","first_computed_at":"2026-05-17T23:40:04.495829Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:04.495829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"19VZuntgHHRCWbEdmDnGShQnbiRxpyNplvjrMYw1IDVuVkW+UaEisv+Wq1+0hQ3PJQ0+sCxzQypy6KaSG9jPAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:04.496345Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.08760","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b687a1c59f07b11a6bd50577f3ea3370dce0680c6471ae09a2a9f16099f9321","sha256:a20f833bde4573c405fdb3ae1aba22eddaa4c3f2a46aa5fa4011f6392cf9c783"],"state_sha256":"e7377eb574349febbc24486e9cb99e1a44fdc54d61fcc8c4a1568548cd734747"}