{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:W3VLICOJMU4AZQNI2QUI63MDSL","short_pith_number":"pith:W3VLICOJ","canonical_record":{"source":{"id":"2111.07879","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2021-11-15T16:34:26Z","cross_cats_sorted":["math.CO","math.MP","math.PR"],"title_canon_sha256":"86c8e40f7b166c2507a82b075a148f41eabb3a2d7b2a2744eea27d19d3954f20","abstract_canon_sha256":"8841927c9172384e5c321d9405533ce0526a85b8da1e28e80841893da5622db7"},"schema_version":"1.0"},"canonical_sha256":"b6eab409c965380cc1a8d4288f6d8392f53eeda2daba84fa12f1febb90f2e2cd","source":{"kind":"arxiv","id":"2111.07879","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:W3VLICOJMU4AZQNI2QUI63MDSL","target":"record","payload":{"canonical_record":{"source":{"id":"2111.07879","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2021-11-15T16:34:26Z","cross_cats_sorted":["math.CO","math.MP","math.PR"],"title_canon_sha256":"86c8e40f7b166c2507a82b075a148f41eabb3a2d7b2a2744eea27d19d3954f20","abstract_canon_sha256":"8841927c9172384e5c321d9405533ce0526a85b8da1e28e80841893da5622db7"},"schema_version":"1.0"},"canonical_sha256":"b6eab409c965380cc1a8d4288f6d8392f53eeda2daba84fa12f1febb90f2e2cd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:02:44.689148Z","signature_b64":"ybm6ZIBBL0yWhV1QlpiGGLz3Um6GCC7WJG1NciYYPQxDbC0IIUKq2scmW/0wMCyK/v6o18aXCFNllgCLZ0IeAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6eab409c965380cc1a8d4288f6d8392f53eeda2daba84fa12f1febb90f2e2cd","last_reissued_at":"2026-07-05T06:02:44.688658Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:02:44.688658Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2111.07879","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":"2026-07-05T06:02:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C457gzVHvMZ/oYPnZvGYqvHRMz/WYDc+jXz+3jnsnOO4wcP7YEKENBDGo5jhQiesWjy0QBsg1HSs6wDdc1v7Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T18:06:58.097757Z"},"content_sha256":"27677dc0de635d80c83c8c4ba16cc8449a88bb72f037a05bc375473a378fc097","schema_version":"1.0","event_id":"sha256:27677dc0de635d80c83c8c4ba16cc8449a88bb72f037a05bc375473a378fc097"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:W3VLICOJMU4AZQNI2QUI63MDSL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the moments of moments of random matrices and Ehrhart polynomials","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Edward Eriksson, Theodoros Assiotis, Wenqi Ni","submitted_at":"2021-11-15T16:34:26Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.07879","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2111.07879/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T06:02:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TApGBe88sNKIN1NGezh5nXx65lj9Cihs/2e/WErTMrqQgY7RaWGidCM7EIhq6/MmGHII3Hbp9Mwt9G2F2i93Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T18:06:58.098135Z"},"content_sha256":"163084de3fc4ab158f69223a86157b7c9a8dfab305453120cce404f5db4f08e5","schema_version":"1.0","event_id":"sha256:163084de3fc4ab158f69223a86157b7c9a8dfab305453120cce404f5db4f08e5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W3VLICOJMU4AZQNI2QUI63MDSL/bundle.json","state_url":"https://pith.science/pith/W3VLICOJMU4AZQNI2QUI63MDSL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W3VLICOJMU4AZQNI2QUI63MDSL/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":"2026-07-06T18:06:58Z","links":{"resolver":"https://pith.science/pith/W3VLICOJMU4AZQNI2QUI63MDSL","bundle":"https://pith.science/pith/W3VLICOJMU4AZQNI2QUI63MDSL/bundle.json","state":"https://pith.science/pith/W3VLICOJMU4AZQNI2QUI63MDSL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W3VLICOJMU4AZQNI2QUI63MDSL/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K9w0RHYCgMVgf79gTpz4LxL2hx/sRd2/ok7TbpPChwUOiWFRZJy2MlnAnQe8GlnBTUQ1Fw/Py7U95zw/pwGfCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T18:06:58.100160Z","bundle_sha256":"d92e08d1c71339ec89755656e3e62b285818e5fb8b3a23ad186a1a497139e252"}}