{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:BXPPR7GHU2PQM656Y5IIF4BLSR","short_pith_number":"pith:BXPPR7GH","schema_version":"1.0","canonical_sha256":"0ddef8fcc7a69f067bbec75082f02b9449fcab56b4efaee39845ff79ee076d64","source":{"kind":"arxiv","id":"1109.5109","version":3},"attestation_state":"computed","paper":{"title":"Surprising Pfaffian factorizations in Random Matrix Theory with Dyson index $\\beta=2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-lat","hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Mario Kieburg","submitted_at":"2011-09-23T15:21:04Z","abstract_excerpt":"In the past decades, determinants and Pfaffians were found for eigenvalue correlations of various random matrix ensembles. These structures simplify the average over a large number of ratios of characteristic polynomials to integrations over one and two characteristic polynomials only. Up to now it was thought that determinants occur for ensembles with Dyson index $\\beta=2$ whereas Pfaffians only for ensembles with $\\beta=1,4$. We derive a non-trivial Pfaffian determinant for $\\beta=2$ random matrix ensembles which is similar to the one for $\\beta=1,4$. Thus, it unveils a hidden universality o"},"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":"1109.5109","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-09-23T15:21:04Z","cross_cats_sorted":["hep-lat","hep-th","math.MP"],"title_canon_sha256":"0e666875bc05f836703dcdbe0bb4cc7554a551b85f570c78ef6e9d1fcbe311af","abstract_canon_sha256":"fcef475b6abde67eba07d31f6e77600f03b647ef47698be20b447adc32f1a745"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:34.410460Z","signature_b64":"FUliHEtSeRAlrPriHKYtGM5KuDunYZ1NiSZXh7MsYuiwfkzWdG6TFgBCH15FGZ6b9isXSjLtYQ0QS8vjdZzdDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ddef8fcc7a69f067bbec75082f02b9449fcab56b4efaee39845ff79ee076d64","last_reissued_at":"2026-05-18T03:17:34.409868Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:34.409868Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Surprising Pfaffian factorizations in Random Matrix Theory with Dyson index $\\beta=2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-lat","hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Mario Kieburg","submitted_at":"2011-09-23T15:21:04Z","abstract_excerpt":"In the past decades, determinants and Pfaffians were found for eigenvalue correlations of various random matrix ensembles. These structures simplify the average over a large number of ratios of characteristic polynomials to integrations over one and two characteristic polynomials only. Up to now it was thought that determinants occur for ensembles with Dyson index $\\beta=2$ whereas Pfaffians only for ensembles with $\\beta=1,4$. We derive a non-trivial Pfaffian determinant for $\\beta=2$ random matrix ensembles which is similar to the one for $\\beta=1,4$. Thus, it unveils a hidden universality o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5109","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1109.5109","created_at":"2026-05-18T03:17:34.409976+00:00"},{"alias_kind":"arxiv_version","alias_value":"1109.5109v3","created_at":"2026-05-18T03:17:34.409976+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5109","created_at":"2026-05-18T03:17:34.409976+00:00"},{"alias_kind":"pith_short_12","alias_value":"BXPPR7GHU2PQ","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_16","alias_value":"BXPPR7GHU2PQM656","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_8","alias_value":"BXPPR7GH","created_at":"2026-05-18T12:26:24.575870+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/BXPPR7GHU2PQM656Y5IIF4BLSR","json":"https://pith.science/pith/BXPPR7GHU2PQM656Y5IIF4BLSR.json","graph_json":"https://pith.science/api/pith-number/BXPPR7GHU2PQM656Y5IIF4BLSR/graph.json","events_json":"https://pith.science/api/pith-number/BXPPR7GHU2PQM656Y5IIF4BLSR/events.json","paper":"https://pith.science/paper/BXPPR7GH"},"agent_actions":{"view_html":"https://pith.science/pith/BXPPR7GHU2PQM656Y5IIF4BLSR","download_json":"https://pith.science/pith/BXPPR7GHU2PQM656Y5IIF4BLSR.json","view_paper":"https://pith.science/paper/BXPPR7GH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1109.5109&json=true","fetch_graph":"https://pith.science/api/pith-number/BXPPR7GHU2PQM656Y5IIF4BLSR/graph.json","fetch_events":"https://pith.science/api/pith-number/BXPPR7GHU2PQM656Y5IIF4BLSR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BXPPR7GHU2PQM656Y5IIF4BLSR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BXPPR7GHU2PQM656Y5IIF4BLSR/action/storage_attestation","attest_author":"https://pith.science/pith/BXPPR7GHU2PQM656Y5IIF4BLSR/action/author_attestation","sign_citation":"https://pith.science/pith/BXPPR7GHU2PQM656Y5IIF4BLSR/action/citation_signature","submit_replication":"https://pith.science/pith/BXPPR7GHU2PQM656Y5IIF4BLSR/action/replication_record"}},"created_at":"2026-05-18T03:17:34.409976+00:00","updated_at":"2026-05-18T03:17:34.409976+00:00"}