{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1994:AEKIHGIG42LGTNACQESSLB3LQB","short_pith_number":"pith:AEKIHGIG","schema_version":"1.0","canonical_sha256":"0114839906e69669b402812525876b804b8954cffc48200be69fe459c7c384f9","source":{"kind":"arxiv","id":"hep-th/9401059","version":1},"attestation_state":"computed","paper":{"title":"The spectrum of the QCD Dirac operator and chiral random matrix theory: the threefold way","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Jacobus Verbaarschot","submitted_at":"1994-01-13T23:11:44Z","abstract_excerpt":"We argue that the spectrum of the QCD Dirac operator near zero virtuality can be described by random matrix theory. As in the case of classical random matrix ensembles of Dyson we have three distinct classes: the chiral orthogonal ensemble (chGOE), the chiral unitary ensemble (chGUE) and the chiral symplectic ensemble (chGSE). They correspond to gauge groups $SU(2)$ in the fundamental representation, $SU(N_c), N_c \\ge 3$ in the fundamental representation, and gauge groups for all $N_c$ in the adjoint representation, respectively. The joint probability density reproduces Leutwyler-Smilga sum ru"},"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":"hep-th/9401059","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1994-01-13T23:11:44Z","cross_cats_sorted":[],"title_canon_sha256":"a19fc0522ef05cb91f557caf7fdd4cee2f7033fa76795d4da80d338a311e6c47","abstract_canon_sha256":"9b9e631d165a3960fc72878d541987703e8a1205a3b46f48c6a803c5d73ce7cc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:18:13.854272Z","signature_b64":"yKb+ZAWFQJoj34x0GKLH8mdE/+ON5jtImZEuT9mMqAgJRxmGy+bEMJx7V/0q7ItujKwRkV0nJXmFya50xI7aCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0114839906e69669b402812525876b804b8954cffc48200be69fe459c7c384f9","last_reissued_at":"2026-05-18T04:18:13.853717Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:18:13.853717Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The spectrum of the QCD Dirac operator and chiral random matrix theory: the threefold way","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Jacobus Verbaarschot","submitted_at":"1994-01-13T23:11:44Z","abstract_excerpt":"We argue that the spectrum of the QCD Dirac operator near zero virtuality can be described by random matrix theory. As in the case of classical random matrix ensembles of Dyson we have three distinct classes: the chiral orthogonal ensemble (chGOE), the chiral unitary ensemble (chGUE) and the chiral symplectic ensemble (chGSE). They correspond to gauge groups $SU(2)$ in the fundamental representation, $SU(N_c), N_c \\ge 3$ in the fundamental representation, and gauge groups for all $N_c$ in the adjoint representation, respectively. The joint probability density reproduces Leutwyler-Smilga sum ru"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9401059","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":""},"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":"hep-th/9401059","created_at":"2026-05-18T04:18:13.853804+00:00"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9401059v1","created_at":"2026-05-18T04:18:13.853804+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9401059","created_at":"2026-05-18T04:18:13.853804+00:00"},{"alias_kind":"pith_short_12","alias_value":"AEKIHGIG42LG","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_16","alias_value":"AEKIHGIG42LGTNAC","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_8","alias_value":"AEKIHGIG","created_at":"2026-05-18T12:25:47.102015+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2006.00200","citing_title":"Analysis of the QCD Kondo phase using random matrices","ref_index":85,"is_internal_anchor":true},{"citing_arxiv_id":"2603.29510","citing_title":"Derivative relations for determinants, Pfaffians and characteristic polynomials in random matrix theory","ref_index":26,"is_internal_anchor":true},{"citing_arxiv_id":"2604.12141","citing_title":"Quantum chaotic systems: a random-matrix approach","ref_index":25,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AEKIHGIG42LGTNACQESSLB3LQB","json":"https://pith.science/pith/AEKIHGIG42LGTNACQESSLB3LQB.json","graph_json":"https://pith.science/api/pith-number/AEKIHGIG42LGTNACQESSLB3LQB/graph.json","events_json":"https://pith.science/api/pith-number/AEKIHGIG42LGTNACQESSLB3LQB/events.json","paper":"https://pith.science/paper/AEKIHGIG"},"agent_actions":{"view_html":"https://pith.science/pith/AEKIHGIG42LGTNACQESSLB3LQB","download_json":"https://pith.science/pith/AEKIHGIG42LGTNACQESSLB3LQB.json","view_paper":"https://pith.science/paper/AEKIHGIG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=hep-th/9401059&json=true","fetch_graph":"https://pith.science/api/pith-number/AEKIHGIG42LGTNACQESSLB3LQB/graph.json","fetch_events":"https://pith.science/api/pith-number/AEKIHGIG42LGTNACQESSLB3LQB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AEKIHGIG42LGTNACQESSLB3LQB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AEKIHGIG42LGTNACQESSLB3LQB/action/storage_attestation","attest_author":"https://pith.science/pith/AEKIHGIG42LGTNACQESSLB3LQB/action/author_attestation","sign_citation":"https://pith.science/pith/AEKIHGIG42LGTNACQESSLB3LQB/action/citation_signature","submit_replication":"https://pith.science/pith/AEKIHGIG42LGTNACQESSLB3LQB/action/replication_record"}},"created_at":"2026-05-18T04:18:13.853804+00:00","updated_at":"2026-05-18T04:18:13.853804+00:00"}