{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:7PXEBT2F7EO52T3BPEFGCVT2JS","short_pith_number":"pith:7PXEBT2F","canonical_record":{"source":{"id":"1207.3909","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-07-17T08:11:59Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"b1360b056f2c3eebdcd72b70b736e5d89cdbcee61604c6c5e9f9e42f7705f7a8","abstract_canon_sha256":"6b6ccbda6793345308570d96cba099b7d68db8e64f310367dfde1ee3e328bd03"},"schema_version":"1.0"},"canonical_sha256":"fbee40cf45f91ddd4f61790a61567a4c93fa2b93b3b7d1568b515adabc934987","source":{"kind":"arxiv","id":"1207.3909","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.3909","created_at":"2026-05-18T03:50:49Z"},{"alias_kind":"arxiv_version","alias_value":"1207.3909v1","created_at":"2026-05-18T03:50:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.3909","created_at":"2026-05-18T03:50:49Z"},{"alias_kind":"pith_short_12","alias_value":"7PXEBT2F7EO5","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"7PXEBT2F7EO52T3B","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"7PXEBT2F","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:7PXEBT2F7EO52T3BPEFGCVT2JS","target":"record","payload":{"canonical_record":{"source":{"id":"1207.3909","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-07-17T08:11:59Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"b1360b056f2c3eebdcd72b70b736e5d89cdbcee61604c6c5e9f9e42f7705f7a8","abstract_canon_sha256":"6b6ccbda6793345308570d96cba099b7d68db8e64f310367dfde1ee3e328bd03"},"schema_version":"1.0"},"canonical_sha256":"fbee40cf45f91ddd4f61790a61567a4c93fa2b93b3b7d1568b515adabc934987","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:50:49.558974Z","signature_b64":"DWdvz3ir6rOx00efnhdCZlx+UXwcj1b+adbKiV3DyZdf31abT5pXRywppeIU1xEoK6+wiG3P0LZ5iCn3aTmSAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fbee40cf45f91ddd4f61790a61567a4c93fa2b93b3b7d1568b515adabc934987","last_reissued_at":"2026-05-18T03:50:49.558159Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:50:49.558159Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.3909","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:50:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0LkpdmiOwJTSUJUkk72vJSssFk6tKD4ZGloJcCpAmd7p/cdzn1J0l4Gy8Kak4+fdePQRvhCo2+cbJ7t8+axVBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T06:33:11.916407Z"},"content_sha256":"31b410ce9f62cc2eda74b52e077a8db1ac2969dbc4de5ac8b5305ca91c09e50a","schema_version":"1.0","event_id":"sha256:31b410ce9f62cc2eda74b52e077a8db1ac2969dbc4de5ac8b5305ca91c09e50a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:7PXEBT2F7EO52T3BPEFGCVT2JS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Zhu's algebra, C_2-algebra and C_2-cofiniteness of parafermion vertex operator algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Ching Hung Lam, Hiromichi Yamada, Tomoyuki Arakawa","submitted_at":"2012-07-17T08:11:59Z","abstract_excerpt":"We determine Zhu's algebra and C_2-algebra of parafermion vertex operator algebras for sl_2. Moreover, we prove the C_2-cofiniteness of parafermion vertex operator algebras for any finite dimensional simple Lie algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3909","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:50:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"582HdXuw1TNLduvKF5aBDoODXwAGoi/LXJWHFwHxSlhIjuzAmLV/zrn9VGu8B8RFuKlFNv1h0hkOutKexoziDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T06:33:11.917126Z"},"content_sha256":"0b0c931f644094696e3ecd8b4402ef34669e3a34b3a357503e9aed535ff56f12","schema_version":"1.0","event_id":"sha256:0b0c931f644094696e3ecd8b4402ef34669e3a34b3a357503e9aed535ff56f12"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7PXEBT2F7EO52T3BPEFGCVT2JS/bundle.json","state_url":"https://pith.science/pith/7PXEBT2F7EO52T3BPEFGCVT2JS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7PXEBT2F7EO52T3BPEFGCVT2JS/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":"2026-06-11T06:33:11Z","links":{"resolver":"https://pith.science/pith/7PXEBT2F7EO52T3BPEFGCVT2JS","bundle":"https://pith.science/pith/7PXEBT2F7EO52T3BPEFGCVT2JS/bundle.json","state":"https://pith.science/pith/7PXEBT2F7EO52T3BPEFGCVT2JS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7PXEBT2F7EO52T3BPEFGCVT2JS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7PXEBT2F7EO52T3BPEFGCVT2JS","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":"6b6ccbda6793345308570d96cba099b7d68db8e64f310367dfde1ee3e328bd03","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-07-17T08:11:59Z","title_canon_sha256":"b1360b056f2c3eebdcd72b70b736e5d89cdbcee61604c6c5e9f9e42f7705f7a8"},"schema_version":"1.0","source":{"id":"1207.3909","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.3909","created_at":"2026-05-18T03:50:49Z"},{"alias_kind":"arxiv_version","alias_value":"1207.3909v1","created_at":"2026-05-18T03:50:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.3909","created_at":"2026-05-18T03:50:49Z"},{"alias_kind":"pith_short_12","alias_value":"7PXEBT2F7EO5","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"7PXEBT2F7EO52T3B","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"7PXEBT2F","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:0b0c931f644094696e3ecd8b4402ef34669e3a34b3a357503e9aed535ff56f12","target":"graph","created_at":"2026-05-18T03:50:49Z","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 determine Zhu's algebra and C_2-algebra of parafermion vertex operator algebras for sl_2. Moreover, we prove the C_2-cofiniteness of parafermion vertex operator algebras for any finite dimensional simple Lie algebras.","authors_text":"Ching Hung Lam, Hiromichi Yamada, Tomoyuki Arakawa","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-07-17T08:11:59Z","title":"Zhu's algebra, C_2-algebra and C_2-cofiniteness of parafermion vertex operator algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3909","kind":"arxiv","version":1},"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":"sha256:31b410ce9f62cc2eda74b52e077a8db1ac2969dbc4de5ac8b5305ca91c09e50a","target":"record","created_at":"2026-05-18T03:50:49Z","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":"6b6ccbda6793345308570d96cba099b7d68db8e64f310367dfde1ee3e328bd03","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-07-17T08:11:59Z","title_canon_sha256":"b1360b056f2c3eebdcd72b70b736e5d89cdbcee61604c6c5e9f9e42f7705f7a8"},"schema_version":"1.0","source":{"id":"1207.3909","kind":"arxiv","version":1}},"canonical_sha256":"fbee40cf45f91ddd4f61790a61567a4c93fa2b93b3b7d1568b515adabc934987","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fbee40cf45f91ddd4f61790a61567a4c93fa2b93b3b7d1568b515adabc934987","first_computed_at":"2026-05-18T03:50:49.558159Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:49.558159Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DWdvz3ir6rOx00efnhdCZlx+UXwcj1b+adbKiV3DyZdf31abT5pXRywppeIU1xEoK6+wiG3P0LZ5iCn3aTmSAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:49.558974Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.3909","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:31b410ce9f62cc2eda74b52e077a8db1ac2969dbc4de5ac8b5305ca91c09e50a","sha256:0b0c931f644094696e3ecd8b4402ef34669e3a34b3a357503e9aed535ff56f12"],"state_sha256":"c6434424a9970a65b3ae0e19b9e5e97c9edf95e26d49c66343f8c7233915de58"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q1UNyKoSkmeayQTzGxe8m/bThY6WvsoMQZPBQnxi3LD4omud94YJ2zBLP9S0VibeurT/BFm3E8a8C/be9OV2AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T06:33:11.921183Z","bundle_sha256":"2e56f84f0d48f927fb1744ee2deec529146280453b62c7cba671e3be5c7e7a7c"}}