{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:2HBH2FKCU2VLGIHFS4JVN47NEA","short_pith_number":"pith:2HBH2FKC","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"},"canonical_sha256":"d1c27d1542a6aab320e5971356f3ed20338e45d3b02ad812b26535ba8ad918d5","source":{"kind":"arxiv","id":"1602.02662","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.02662","created_at":"2026-05-18T00:51:17Z"},{"alias_kind":"arxiv_version","alias_value":"1602.02662v3","created_at":"2026-05-18T00:51:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.02662","created_at":"2026-05-18T00:51:17Z"},{"alias_kind":"pith_short_12","alias_value":"2HBH2FKCU2VL","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2HBH2FKCU2VLGIHF","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2HBH2FKC","created_at":"2026-05-18T12:29:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:2HBH2FKCU2VLGIHFS4JVN47NEA","target":"record","payload":{"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"},"canonical_sha256":"d1c27d1542a6aab320e5971356f3ed20338e45d3b02ad812b26535ba8ad918d5","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"},"source_kind":"arxiv","source_id":"1602.02662","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":"2026-05-18T00:51:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tV36P3lOoss4Ox5JviitjHMdNmQVx4H7cICOUJr+A9QWvFhD9xBxYRmG2SwTN36WLp5FbPU3tAtSifbB1mo0Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T16:24:57.932586Z"},"content_sha256":"cae09ddf7318cc9a8d2f42a9c2340671175458d7399aae960702391e6f5836ad","schema_version":"1.0","event_id":"sha256:cae09ddf7318cc9a8d2f42a9c2340671175458d7399aae960702391e6f5836ad"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:2HBH2FKCU2VLGIHFS4JVN47NEA","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:51:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ph0V2dqohFI75t/nquJi8J4fUX+AUj23r656kTHzsbA7Gx/vzdg/KR1wgeU7A2VxNgKhYJLQix5LHbl/XxoOAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T16:24:57.932941Z"},"content_sha256":"fa88eacaae0c2234f3bd65f059d9719b52bc4ebe1787c9946bb16cf4e1fe6ae8","schema_version":"1.0","event_id":"sha256:fa88eacaae0c2234f3bd65f059d9719b52bc4ebe1787c9946bb16cf4e1fe6ae8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2HBH2FKCU2VLGIHFS4JVN47NEA/bundle.json","state_url":"https://pith.science/pith/2HBH2FKCU2VLGIHFS4JVN47NEA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2HBH2FKCU2VLGIHFS4JVN47NEA/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":"2026-05-19T16:24:57Z","links":{"resolver":"https://pith.science/pith/2HBH2FKCU2VLGIHFS4JVN47NEA","bundle":"https://pith.science/pith/2HBH2FKCU2VLGIHFS4JVN47NEA/bundle.json","state":"https://pith.science/pith/2HBH2FKCU2VLGIHFS4JVN47NEA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2HBH2FKCU2VLGIHFS4JVN47NEA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2HBH2FKCU2VLGIHFS4JVN47NEA","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":"4ce15e97f454e83ab39ab2b6b2c1b2a8fe903b4c129b9d71b73dcf02415b4e76","cross_cats_sorted":["cond-mat.mes-hall","hep-th","math-ph","math.MP","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-02-08T17:41:48Z","title_canon_sha256":"7ef7a6045f68029280f85ae273f3deb7189c67e32f454aeb2573b8724423194b"},"schema_version":"1.0","source":{"id":"1602.02662","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.02662","created_at":"2026-05-18T00:51:17Z"},{"alias_kind":"arxiv_version","alias_value":"1602.02662v3","created_at":"2026-05-18T00:51:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.02662","created_at":"2026-05-18T00:51:17Z"},{"alias_kind":"pith_short_12","alias_value":"2HBH2FKCU2VL","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2HBH2FKCU2VLGIHF","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2HBH2FKC","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:fa88eacaae0c2234f3bd65f059d9719b52bc4ebe1787c9946bb16cf4e1fe6ae8","target":"graph","created_at":"2026-05-18T00:51:17Z","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":"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","authors_text":"Arthur Jaffe, Zhengwei Liu","cross_cats":["cond-mat.mes-hall","hep-th","math-ph","math.MP","math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-02-08T17:41:48Z","title":"Planar Para Algebras, Reflection Positivity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02662","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:cae09ddf7318cc9a8d2f42a9c2340671175458d7399aae960702391e6f5836ad","target":"record","created_at":"2026-05-18T00:51:17Z","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":"4ce15e97f454e83ab39ab2b6b2c1b2a8fe903b4c129b9d71b73dcf02415b4e76","cross_cats_sorted":["cond-mat.mes-hall","hep-th","math-ph","math.MP","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-02-08T17:41:48Z","title_canon_sha256":"7ef7a6045f68029280f85ae273f3deb7189c67e32f454aeb2573b8724423194b"},"schema_version":"1.0","source":{"id":"1602.02662","kind":"arxiv","version":3}},"canonical_sha256":"d1c27d1542a6aab320e5971356f3ed20338e45d3b02ad812b26535ba8ad918d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1c27d1542a6aab320e5971356f3ed20338e45d3b02ad812b26535ba8ad918d5","first_computed_at":"2026-05-18T00:51:17.976988Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:17.976988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JoqhAD0pSlshQOruYCWDDwu0ZRCS6W3H19NWS2IOZ/BC7DAi9cDWbEWeYvb3ZE6XNKQdGKOI8UN7u+8pyGNpCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:17.977719Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.02662","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cae09ddf7318cc9a8d2f42a9c2340671175458d7399aae960702391e6f5836ad","sha256:fa88eacaae0c2234f3bd65f059d9719b52bc4ebe1787c9946bb16cf4e1fe6ae8"],"state_sha256":"8699590e2baa14c1a68a7767e4b4d4a69a0d4e8ea7ae976b4950944fb4fa46fe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1tsii8S/7q1jMgV8wrijRKsbK+voDwq94Psgci7SUsal5Vv1KQ0BZBqmyrYNJNvS10kxGCfobq5wrUQXf4BcAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-19T16:24:57.934973Z","bundle_sha256":"8a12f6dddd96ccfdf267645f27092232217e93b52b3a3c8c7a0028348a72ee7a"}}