{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:BXPPR7GHU2PQM656Y5IIF4BLSR","short_pith_number":"pith:BXPPR7GH","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"},"canonical_sha256":"0ddef8fcc7a69f067bbec75082f02b9449fcab56b4efaee39845ff79ee076d64","source":{"kind":"arxiv","id":"1109.5109","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.5109","created_at":"2026-05-18T03:17:34Z"},{"alias_kind":"arxiv_version","alias_value":"1109.5109v3","created_at":"2026-05-18T03:17:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5109","created_at":"2026-05-18T03:17:34Z"},{"alias_kind":"pith_short_12","alias_value":"BXPPR7GHU2PQ","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"BXPPR7GHU2PQM656","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"BXPPR7GH","created_at":"2026-05-18T12:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:BXPPR7GHU2PQM656Y5IIF4BLSR","target":"record","payload":{"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"},"canonical_sha256":"0ddef8fcc7a69f067bbec75082f02b9449fcab56b4efaee39845ff79ee076d64","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"},"source_kind":"arxiv","source_id":"1109.5109","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:17:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8lr+LQwhcYZnP/8VYZC/CJTn0jAPtVhAydAJm7KNU3c/wiIyzvHmiMvaN3+hsaQG43hLkadQOWq2PB+5Hb+8BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T22:24:26.411724Z"},"content_sha256":"3bdc6a1514f4870f0b4dcf04ded48f91911e992039eb036c39322de1f1358e9e","schema_version":"1.0","event_id":"sha256:3bdc6a1514f4870f0b4dcf04ded48f91911e992039eb036c39322de1f1358e9e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:BXPPR7GHU2PQM656Y5IIF4BLSR","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:17:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MkzihjKUNLX9+5a1rqOJd6JIDAofujG++nEhEG8sNniYw+ERU4PSsH7XruBFYpkl/dWg/xuXJeVgFb22DxFRBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T22:24:26.412104Z"},"content_sha256":"675eb977bf6bc8e69dc02d77086c89a1a61756ca778475e90e38d8962a21f39f","schema_version":"1.0","event_id":"sha256:675eb977bf6bc8e69dc02d77086c89a1a61756ca778475e90e38d8962a21f39f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BXPPR7GHU2PQM656Y5IIF4BLSR/bundle.json","state_url":"https://pith.science/pith/BXPPR7GHU2PQM656Y5IIF4BLSR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BXPPR7GHU2PQM656Y5IIF4BLSR/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":"2026-05-23T22:24:26Z","links":{"resolver":"https://pith.science/pith/BXPPR7GHU2PQM656Y5IIF4BLSR","bundle":"https://pith.science/pith/BXPPR7GHU2PQM656Y5IIF4BLSR/bundle.json","state":"https://pith.science/pith/BXPPR7GHU2PQM656Y5IIF4BLSR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BXPPR7GHU2PQM656Y5IIF4BLSR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:BXPPR7GHU2PQM656Y5IIF4BLSR","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":"fcef475b6abde67eba07d31f6e77600f03b647ef47698be20b447adc32f1a745","cross_cats_sorted":["hep-lat","hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-09-23T15:21:04Z","title_canon_sha256":"0e666875bc05f836703dcdbe0bb4cc7554a551b85f570c78ef6e9d1fcbe311af"},"schema_version":"1.0","source":{"id":"1109.5109","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.5109","created_at":"2026-05-18T03:17:34Z"},{"alias_kind":"arxiv_version","alias_value":"1109.5109v3","created_at":"2026-05-18T03:17:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5109","created_at":"2026-05-18T03:17:34Z"},{"alias_kind":"pith_short_12","alias_value":"BXPPR7GHU2PQ","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"BXPPR7GHU2PQM656","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"BXPPR7GH","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:675eb977bf6bc8e69dc02d77086c89a1a61756ca778475e90e38d8962a21f39f","target":"graph","created_at":"2026-05-18T03:17:34Z","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"},"paper":{"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","authors_text":"Mario Kieburg","cross_cats":["hep-lat","hep-th","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-09-23T15:21:04Z","title":"Surprising Pfaffian factorizations in Random Matrix Theory with Dyson index $\\beta=2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5109","kind":"arxiv","version":3},"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":"sha256:3bdc6a1514f4870f0b4dcf04ded48f91911e992039eb036c39322de1f1358e9e","target":"record","created_at":"2026-05-18T03:17:34Z","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":"fcef475b6abde67eba07d31f6e77600f03b647ef47698be20b447adc32f1a745","cross_cats_sorted":["hep-lat","hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-09-23T15:21:04Z","title_canon_sha256":"0e666875bc05f836703dcdbe0bb4cc7554a551b85f570c78ef6e9d1fcbe311af"},"schema_version":"1.0","source":{"id":"1109.5109","kind":"arxiv","version":3}},"canonical_sha256":"0ddef8fcc7a69f067bbec75082f02b9449fcab56b4efaee39845ff79ee076d64","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ddef8fcc7a69f067bbec75082f02b9449fcab56b4efaee39845ff79ee076d64","first_computed_at":"2026-05-18T03:17:34.409868Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:34.409868Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FUliHEtSeRAlrPriHKYtGM5KuDunYZ1NiSZXh7MsYuiwfkzWdG6TFgBCH15FGZ6b9isXSjLtYQ0QS8vjdZzdDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:34.410460Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.5109","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3bdc6a1514f4870f0b4dcf04ded48f91911e992039eb036c39322de1f1358e9e","sha256:675eb977bf6bc8e69dc02d77086c89a1a61756ca778475e90e38d8962a21f39f"],"state_sha256":"475e7261c0732e28aa4c7949848cffd65177240993963e9ce94c13297cb506b0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"npHhYQhm3JNSR2ESBxobezQA4cnmMxMCFHl2F0zaEhFQ94TKJRZqu0iYP85oPrTH6LaMXF8gOvBZg7HJDUI0Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T22:24:26.416083Z","bundle_sha256":"e4a9ab8b1b2d5f10f18a411008066344e22cf386f113137a99defc328019ced9"}}