{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:T2NXBBSOX2XPZWU5GA3AAZQ65Q","short_pith_number":"pith:T2NXBBSO","schema_version":"1.0","canonical_sha256":"9e9b70864ebeaefcda9d303600661eec3d16b869a4671337329543cfdd022748","source":{"kind":"arxiv","id":"2505.21376","version":1},"attestation_state":"computed","paper":{"title":"Addition to \"Structured random matrices and cyclic cumulants: A free probability approach\"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Denis Bernard, Ludwig Hruza","submitted_at":"2025-05-27T16:05:48Z","abstract_excerpt":"We give a refined definition of the class of random matrix ensembles introduced in our paper \"Structured random matrices and cyclic cumulants: A free probability approach\" (arXiv:2309.14315) by extending the so-called fourth axiom to deal with cumulants of disjoint cycles. We argue that the theorems concerning the stability of such ensembles under non-linear transformations still hold with these refined axioms."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2505.21376","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-05-27T16:05:48Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"4b62554b166b04155585d2eb13073b615664ed798d128c02b8cdc8ecccfaf9ba","abstract_canon_sha256":"55947f57c5d98218638726681a68a1f3a5575c3512daa7555de18667d5742baf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:10:40.975732Z","signature_b64":"hGgZGmUP/OFBcbPuzzsjCBygr0BS8Yqp0B/V4oM5l2qB+H19lqszaaqrd8grj/myXghpz1AKsR3/1hjw1eUDAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e9b70864ebeaefcda9d303600661eec3d16b869a4671337329543cfdd022748","last_reissued_at":"2026-07-05T11:10:40.975115Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:10:40.975115Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Addition to \"Structured random matrices and cyclic cumulants: A free probability approach\"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Denis Bernard, Ludwig Hruza","submitted_at":"2025-05-27T16:05:48Z","abstract_excerpt":"We give a refined definition of the class of random matrix ensembles introduced in our paper \"Structured random matrices and cyclic cumulants: A free probability approach\" (arXiv:2309.14315) by extending the so-called fourth axiom to deal with cumulants of disjoint cycles. We argue that the theorems concerning the stability of such ensembles under non-linear transformations still hold with these refined axioms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.21376","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.21376/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2505.21376","created_at":"2026-07-05T11:10:40.975173+00:00"},{"alias_kind":"arxiv_version","alias_value":"2505.21376v1","created_at":"2026-07-05T11:10:40.975173+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.21376","created_at":"2026-07-05T11:10:40.975173+00:00"},{"alias_kind":"pith_short_12","alias_value":"T2NXBBSOX2XP","created_at":"2026-07-05T11:10:40.975173+00:00"},{"alias_kind":"pith_short_16","alias_value":"T2NXBBSOX2XPZWU5","created_at":"2026-07-05T11:10:40.975173+00:00"},{"alias_kind":"pith_short_8","alias_value":"T2NXBBSO","created_at":"2026-07-05T11:10:40.975173+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/T2NXBBSOX2XPZWU5GA3AAZQ65Q","json":"https://pith.science/pith/T2NXBBSOX2XPZWU5GA3AAZQ65Q.json","graph_json":"https://pith.science/api/pith-number/T2NXBBSOX2XPZWU5GA3AAZQ65Q/graph.json","events_json":"https://pith.science/api/pith-number/T2NXBBSOX2XPZWU5GA3AAZQ65Q/events.json","paper":"https://pith.science/paper/T2NXBBSO"},"agent_actions":{"view_html":"https://pith.science/pith/T2NXBBSOX2XPZWU5GA3AAZQ65Q","download_json":"https://pith.science/pith/T2NXBBSOX2XPZWU5GA3AAZQ65Q.json","view_paper":"https://pith.science/paper/T2NXBBSO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2505.21376&json=true","fetch_graph":"https://pith.science/api/pith-number/T2NXBBSOX2XPZWU5GA3AAZQ65Q/graph.json","fetch_events":"https://pith.science/api/pith-number/T2NXBBSOX2XPZWU5GA3AAZQ65Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T2NXBBSOX2XPZWU5GA3AAZQ65Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T2NXBBSOX2XPZWU5GA3AAZQ65Q/action/storage_attestation","attest_author":"https://pith.science/pith/T2NXBBSOX2XPZWU5GA3AAZQ65Q/action/author_attestation","sign_citation":"https://pith.science/pith/T2NXBBSOX2XPZWU5GA3AAZQ65Q/action/citation_signature","submit_replication":"https://pith.science/pith/T2NXBBSOX2XPZWU5GA3AAZQ65Q/action/replication_record"}},"created_at":"2026-07-05T11:10:40.975173+00:00","updated_at":"2026-07-05T11:10:40.975173+00:00"}