{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:W3VLICOJMU4AZQNI2QUI63MDSL","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":"8841927c9172384e5c321d9405533ce0526a85b8da1e28e80841893da5622db7","cross_cats_sorted":["math.CO","math.MP","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2021-11-15T16:34:26Z","title_canon_sha256":"86c8e40f7b166c2507a82b075a148f41eabb3a2d7b2a2744eea27d19d3954f20"},"schema_version":"1.0","source":{"id":"2111.07879","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.07879","created_at":"2026-07-05T06:02:44Z"},{"alias_kind":"arxiv_version","alias_value":"2111.07879v2","created_at":"2026-07-05T06:02:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.07879","created_at":"2026-07-05T06:02:44Z"},{"alias_kind":"pith_short_12","alias_value":"W3VLICOJMU4A","created_at":"2026-07-05T06:02:44Z"},{"alias_kind":"pith_short_16","alias_value":"W3VLICOJMU4AZQNI","created_at":"2026-07-05T06:02:44Z"},{"alias_kind":"pith_short_8","alias_value":"W3VLICOJ","created_at":"2026-07-05T06:02:44Z"}],"graph_snapshots":[{"event_id":"sha256:163084de3fc4ab158f69223a86157b7c9a8dfab305453120cce404f5db4f08e5","target":"graph","created_at":"2026-07-05T06:02:44Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2111.07879/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"There has been significant interest in studying the asymptotics of certain generalised moments, called the moments of moments, of characteristic polynomials of random Haar-distributed unitary and symplectic matrices, as the matrix size $N$ goes to infinity. These quantities depend on two parameters $k$ and $q$ and when both of them are positive integers it has been shown that these moments are in fact polynomials in the matrix size $N$. In this paper we classify the integer roots of these polynomials and moreover prove that the polynomials themselves satisfy a certain symmetry property. This c","authors_text":"Edward Eriksson, Theodoros Assiotis, Wenqi Ni","cross_cats":["math.CO","math.MP","math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2021-11-15T16:34:26Z","title":"On the moments of moments of random matrices and Ehrhart polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.07879","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":"sha256:27677dc0de635d80c83c8c4ba16cc8449a88bb72f037a05bc375473a378fc097","target":"record","created_at":"2026-07-05T06:02:44Z","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":"8841927c9172384e5c321d9405533ce0526a85b8da1e28e80841893da5622db7","cross_cats_sorted":["math.CO","math.MP","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2021-11-15T16:34:26Z","title_canon_sha256":"86c8e40f7b166c2507a82b075a148f41eabb3a2d7b2a2744eea27d19d3954f20"},"schema_version":"1.0","source":{"id":"2111.07879","kind":"arxiv","version":2}},"canonical_sha256":"b6eab409c965380cc1a8d4288f6d8392f53eeda2daba84fa12f1febb90f2e2cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b6eab409c965380cc1a8d4288f6d8392f53eeda2daba84fa12f1febb90f2e2cd","first_computed_at":"2026-07-05T06:02:44.688658Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:02:44.688658Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ybm6ZIBBL0yWhV1QlpiGGLz3Um6GCC7WJG1NciYYPQxDbC0IIUKq2scmW/0wMCyK/v6o18aXCFNllgCLZ0IeAg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:02:44.689148Z","signed_message":"canonical_sha256_bytes"},"source_id":"2111.07879","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:27677dc0de635d80c83c8c4ba16cc8449a88bb72f037a05bc375473a378fc097","sha256:163084de3fc4ab158f69223a86157b7c9a8dfab305453120cce404f5db4f08e5"],"state_sha256":"96d5a3e65f7b7a1bacd881b2c9713482606c696d8926a74a7328a33aab3d911e"}