{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:2HBH2FKCU2VLGIHFS4JVN47NEA","short_pith_number":"pith:2HBH2FKC","schema_version":"1.0","canonical_sha256":"d1c27d1542a6aab320e5971356f3ed20338e45d3b02ad812b26535ba8ad918d5","source":{"kind":"arxiv","id":"1602.02662","version":3},"attestation_state":"computed","paper":{"title":"Planar Para Algebras, Reflection Positivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mes-hall","hep-th","math-ph","math.MP","math.OA"],"primary_cat":"math.QA","authors_text":"Arthur Jaffe, Zhengwei Liu","submitted_at":"2016-02-08T17:41:48Z","abstract_excerpt":"We define a planar para algebra, which arises naturally from combining planar algebras with the idea of $\\mathbb{Z}_{N}$ para symmetry in physics. A subfactor planar para algebra is a Hilbert space representation of planar tangles with parafermionic defects, that are invariant under para isotopy. For each $\\mathbb{Z}_{N}$, we construct a family of subfactor planar para algebras which play the role of Temperley-Lieb-Jones planar algebras. The first example in this family is the parafermion planar para algebra (PAPPA). Based on this example, we introduce parafermion Pauli matrices, quaternion re"},"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":"1602.02662","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-02-08T17:41:48Z","cross_cats_sorted":["cond-mat.mes-hall","hep-th","math-ph","math.MP","math.OA"],"title_canon_sha256":"7ef7a6045f68029280f85ae273f3deb7189c67e32f454aeb2573b8724423194b","abstract_canon_sha256":"4ce15e97f454e83ab39ab2b6b2c1b2a8fe903b4c129b9d71b73dcf02415b4e76"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:17.977719Z","signature_b64":"JoqhAD0pSlshQOruYCWDDwu0ZRCS6W3H19NWS2IOZ/BC7DAi9cDWbEWeYvb3ZE6XNKQdGKOI8UN7u+8pyGNpCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1c27d1542a6aab320e5971356f3ed20338e45d3b02ad812b26535ba8ad918d5","last_reissued_at":"2026-05-18T00:51:17.976988Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:17.976988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Planar Para Algebras, Reflection Positivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mes-hall","hep-th","math-ph","math.MP","math.OA"],"primary_cat":"math.QA","authors_text":"Arthur Jaffe, Zhengwei Liu","submitted_at":"2016-02-08T17:41:48Z","abstract_excerpt":"We define a planar para algebra, which arises naturally from combining planar algebras with the idea of $\\mathbb{Z}_{N}$ para symmetry in physics. A subfactor planar para algebra is a Hilbert space representation of planar tangles with parafermionic defects, that are invariant under para isotopy. For each $\\mathbb{Z}_{N}$, we construct a family of subfactor planar para algebras which play the role of Temperley-Lieb-Jones planar algebras. The first example in this family is the parafermion planar para algebra (PAPPA). Based on this example, we introduce parafermion Pauli matrices, quaternion re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02662","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":"1602.02662","created_at":"2026-05-18T00:51:17.977118+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.02662v3","created_at":"2026-05-18T00:51:17.977118+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.02662","created_at":"2026-05-18T00:51:17.977118+00:00"},{"alias_kind":"pith_short_12","alias_value":"2HBH2FKCU2VL","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_16","alias_value":"2HBH2FKCU2VLGIHF","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_8","alias_value":"2HBH2FKC","created_at":"2026-05-18T12:29:55.572404+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/2HBH2FKCU2VLGIHFS4JVN47NEA","json":"https://pith.science/pith/2HBH2FKCU2VLGIHFS4JVN47NEA.json","graph_json":"https://pith.science/api/pith-number/2HBH2FKCU2VLGIHFS4JVN47NEA/graph.json","events_json":"https://pith.science/api/pith-number/2HBH2FKCU2VLGIHFS4JVN47NEA/events.json","paper":"https://pith.science/paper/2HBH2FKC"},"agent_actions":{"view_html":"https://pith.science/pith/2HBH2FKCU2VLGIHFS4JVN47NEA","download_json":"https://pith.science/pith/2HBH2FKCU2VLGIHFS4JVN47NEA.json","view_paper":"https://pith.science/paper/2HBH2FKC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.02662&json=true","fetch_graph":"https://pith.science/api/pith-number/2HBH2FKCU2VLGIHFS4JVN47NEA/graph.json","fetch_events":"https://pith.science/api/pith-number/2HBH2FKCU2VLGIHFS4JVN47NEA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2HBH2FKCU2VLGIHFS4JVN47NEA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2HBH2FKCU2VLGIHFS4JVN47NEA/action/storage_attestation","attest_author":"https://pith.science/pith/2HBH2FKCU2VLGIHFS4JVN47NEA/action/author_attestation","sign_citation":"https://pith.science/pith/2HBH2FKCU2VLGIHFS4JVN47NEA/action/citation_signature","submit_replication":"https://pith.science/pith/2HBH2FKCU2VLGIHFS4JVN47NEA/action/replication_record"}},"created_at":"2026-05-18T00:51:17.977118+00:00","updated_at":"2026-05-18T00:51:17.977118+00:00"}