{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:XWXPHLLWVPG4KKPXCH22YDFQYB","short_pith_number":"pith:XWXPHLLW","schema_version":"1.0","canonical_sha256":"bdaef3ad76abcdc529f711f5ac0cb0c06769dafacb50561f8baad46ce8261df8","source":{"kind":"arxiv","id":"2301.05022","version":1},"attestation_state":"computed","paper":{"title":"Progress on the study of the Ginibre ensembles II: GinOE and GinSE","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Peter J. Forrester, Sung-Soo Byun","submitted_at":"2023-01-12T13:51:19Z","abstract_excerpt":"This is part II of a review relating to the three classes of random non-Hermitian Gaussian matrices introduced by Ginibre in 1965. While part I restricted attention to the GinUE (Ginibre unitary ensemble) case of complex elements, in this part the cases of real elements (GinOE, denoting Ginibre orthogonal ensemble) and quaternion elements represented as $2 \\times 2$ complex blocks (GinSE, denoting Ginibre symplectic ensemble) are considered. The eigenvalues of both GinOE and GinSE form Pfaffian point processes, which are more complicated than the determinantal point processes resulting from Gi"},"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":"2301.05022","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2023-01-12T13:51:19Z","cross_cats_sorted":["math.MP","math.PR"],"title_canon_sha256":"9bf94191f45dbff65b4f749e7ea88948b6eafa5311b80bc9ed1826c0f1b71617","abstract_canon_sha256":"6b1c2da3f55a2a220ab1a5333f3fd6c582c77bc323d5bfd69a559ec581435b32"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:32:38.744268Z","signature_b64":"TeT2zervYUM6dQ60+Rcjx6Fz0dh6Pri+PXT3l9bBdaM1Yr7KdUMS4HVQoOD0O2+AoSRBj4FTok8Tk0snrIecAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bdaef3ad76abcdc529f711f5ac0cb0c06769dafacb50561f8baad46ce8261df8","last_reissued_at":"2026-07-05T05:32:38.743759Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:32:38.743759Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Progress on the study of the Ginibre ensembles II: GinOE and GinSE","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Peter J. Forrester, Sung-Soo Byun","submitted_at":"2023-01-12T13:51:19Z","abstract_excerpt":"This is part II of a review relating to the three classes of random non-Hermitian Gaussian matrices introduced by Ginibre in 1965. While part I restricted attention to the GinUE (Ginibre unitary ensemble) case of complex elements, in this part the cases of real elements (GinOE, denoting Ginibre orthogonal ensemble) and quaternion elements represented as $2 \\times 2$ complex blocks (GinSE, denoting Ginibre symplectic ensemble) are considered. The eigenvalues of both GinOE and GinSE form Pfaffian point processes, which are more complicated than the determinantal point processes resulting from Gi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.05022","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/2301.05022/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":"2301.05022","created_at":"2026-07-05T05:32:38.743827+00:00"},{"alias_kind":"arxiv_version","alias_value":"2301.05022v1","created_at":"2026-07-05T05:32:38.743827+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2301.05022","created_at":"2026-07-05T05:32:38.743827+00:00"},{"alias_kind":"pith_short_12","alias_value":"XWXPHLLWVPG4","created_at":"2026-07-05T05:32:38.743827+00:00"},{"alias_kind":"pith_short_16","alias_value":"XWXPHLLWVPG4KKPX","created_at":"2026-07-05T05:32:38.743827+00:00"},{"alias_kind":"pith_short_8","alias_value":"XWXPHLLW","created_at":"2026-07-05T05:32:38.743827+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.25736","citing_title":"Spectral properties of non-Hermitian real random matrices with long-range correlations","ref_index":33,"is_internal_anchor":false},{"citing_arxiv_id":"2306.00300","citing_title":"Eigenvalues, eigenvector-overlaps, and regularized Fuglede-Kadison determinant of the non-Hermitian matrix-valued Brownian motion","ref_index":10,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XWXPHLLWVPG4KKPXCH22YDFQYB","json":"https://pith.science/pith/XWXPHLLWVPG4KKPXCH22YDFQYB.json","graph_json":"https://pith.science/api/pith-number/XWXPHLLWVPG4KKPXCH22YDFQYB/graph.json","events_json":"https://pith.science/api/pith-number/XWXPHLLWVPG4KKPXCH22YDFQYB/events.json","paper":"https://pith.science/paper/XWXPHLLW"},"agent_actions":{"view_html":"https://pith.science/pith/XWXPHLLWVPG4KKPXCH22YDFQYB","download_json":"https://pith.science/pith/XWXPHLLWVPG4KKPXCH22YDFQYB.json","view_paper":"https://pith.science/paper/XWXPHLLW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2301.05022&json=true","fetch_graph":"https://pith.science/api/pith-number/XWXPHLLWVPG4KKPXCH22YDFQYB/graph.json","fetch_events":"https://pith.science/api/pith-number/XWXPHLLWVPG4KKPXCH22YDFQYB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XWXPHLLWVPG4KKPXCH22YDFQYB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XWXPHLLWVPG4KKPXCH22YDFQYB/action/storage_attestation","attest_author":"https://pith.science/pith/XWXPHLLWVPG4KKPXCH22YDFQYB/action/author_attestation","sign_citation":"https://pith.science/pith/XWXPHLLWVPG4KKPXCH22YDFQYB/action/citation_signature","submit_replication":"https://pith.science/pith/XWXPHLLWVPG4KKPXCH22YDFQYB/action/replication_record"}},"created_at":"2026-07-05T05:32:38.743827+00:00","updated_at":"2026-07-05T05:32:38.743827+00:00"}