{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:J7LT3AGPWG75ZITE3KNDNRHFRF","short_pith_number":"pith:J7LT3AGP","schema_version":"1.0","canonical_sha256":"4fd73d80cfb1bfdca264da9a36c4e5896909876edb37853939c58cb80c92ef7a","source":{"kind":"arxiv","id":"hep-th/0506199","version":4},"attestation_state":"computed","paper":{"title":"The Z_k^(su(2),3/2) Parafermions","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"P. Jacob, P. Mathieu","submitted_at":"2005-06-23T19:35:01Z","abstract_excerpt":"We introduce a novel parafermionic theory for which the conformal dimension of the basic parafermion is 3(1-1/k)/2, with k even. The structure constants and the central charges are obtained from mode-type associativity calculations. The spectrum of the completely reducible representations is also determined. The primary fields turns out to be labeled by two positive integers instead of a single one for the usual parafermionic models. The simplest singular vectors are also displayed. It is argued that these models are equivalent to the non-unitary minimal W_k(k+1,k+3) models. More generally, we"},"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/0506199","kind":"arxiv","version":4},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2005-06-23T19:35:01Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"06f222ac4529c01dc1b47268dc83028d39d98b0b63889f27ab240499a723d9e8","abstract_canon_sha256":"6bee898872facb0c75d537458c25820adea24fafbe48a37882963e883b83f8a0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:56.929947Z","signature_b64":"sAn+NzYgvqCW9GRY+p9q5rh241CsExmjWImTSPRxdzvzYZLNDoUwKD/CmOIvmmM4JcEWXv7G/aSIw5Mv4FCyCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4fd73d80cfb1bfdca264da9a36c4e5896909876edb37853939c58cb80c92ef7a","last_reissued_at":"2026-05-18T01:05:56.929546Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:56.929546Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Z_k^(su(2),3/2) Parafermions","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"P. Jacob, P. Mathieu","submitted_at":"2005-06-23T19:35:01Z","abstract_excerpt":"We introduce a novel parafermionic theory for which the conformal dimension of the basic parafermion is 3(1-1/k)/2, with k even. The structure constants and the central charges are obtained from mode-type associativity calculations. The spectrum of the completely reducible representations is also determined. The primary fields turns out to be labeled by two positive integers instead of a single one for the usual parafermionic models. The simplest singular vectors are also displayed. It is argued that these models are equivalent to the non-unitary minimal W_k(k+1,k+3) models. More generally, we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0506199","kind":"arxiv","version":4},"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/0506199","created_at":"2026-05-18T01:05:56.929612+00:00"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0506199v4","created_at":"2026-05-18T01:05:56.929612+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0506199","created_at":"2026-05-18T01:05:56.929612+00:00"},{"alias_kind":"pith_short_12","alias_value":"J7LT3AGPWG75","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_16","alias_value":"J7LT3AGPWG75ZITE","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_8","alias_value":"J7LT3AGP","created_at":"2026-05-18T12:25:53.335082+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/J7LT3AGPWG75ZITE3KNDNRHFRF","json":"https://pith.science/pith/J7LT3AGPWG75ZITE3KNDNRHFRF.json","graph_json":"https://pith.science/api/pith-number/J7LT3AGPWG75ZITE3KNDNRHFRF/graph.json","events_json":"https://pith.science/api/pith-number/J7LT3AGPWG75ZITE3KNDNRHFRF/events.json","paper":"https://pith.science/paper/J7LT3AGP"},"agent_actions":{"view_html":"https://pith.science/pith/J7LT3AGPWG75ZITE3KNDNRHFRF","download_json":"https://pith.science/pith/J7LT3AGPWG75ZITE3KNDNRHFRF.json","view_paper":"https://pith.science/paper/J7LT3AGP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=hep-th/0506199&json=true","fetch_graph":"https://pith.science/api/pith-number/J7LT3AGPWG75ZITE3KNDNRHFRF/graph.json","fetch_events":"https://pith.science/api/pith-number/J7LT3AGPWG75ZITE3KNDNRHFRF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J7LT3AGPWG75ZITE3KNDNRHFRF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J7LT3AGPWG75ZITE3KNDNRHFRF/action/storage_attestation","attest_author":"https://pith.science/pith/J7LT3AGPWG75ZITE3KNDNRHFRF/action/author_attestation","sign_citation":"https://pith.science/pith/J7LT3AGPWG75ZITE3KNDNRHFRF/action/citation_signature","submit_replication":"https://pith.science/pith/J7LT3AGPWG75ZITE3KNDNRHFRF/action/replication_record"}},"created_at":"2026-05-18T01:05:56.929612+00:00","updated_at":"2026-05-18T01:05:56.929612+00:00"}