{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:NRXOY4N4EA52VIMLUYCR6NMFRY","short_pith_number":"pith:NRXOY4N4","canonical_record":{"source":{"id":"1810.04790","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-10-10T03:16:01Z","cross_cats_sorted":[],"title_canon_sha256":"d2e423b3520e7bbf580938b05e8c35e915b2f661ca029b0318bb2f5e293d6170","abstract_canon_sha256":"7e75283e6aeba2d8779889907424be3d2bea92696e796c1d71a73879b964e0da"},"schema_version":"1.0"},"canonical_sha256":"6c6eec71bc203baaa18ba6051f35858e1440b8ecdb34cc527219a842e6088707","source":{"kind":"arxiv","id":"1810.04790","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.04790","created_at":"2026-05-18T00:03:35Z"},{"alias_kind":"arxiv_version","alias_value":"1810.04790v1","created_at":"2026-05-18T00:03:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.04790","created_at":"2026-05-18T00:03:35Z"},{"alias_kind":"pith_short_12","alias_value":"NRXOY4N4EA52","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NRXOY4N4EA52VIML","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NRXOY4N4","created_at":"2026-05-18T12:32:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:NRXOY4N4EA52VIMLUYCR6NMFRY","target":"record","payload":{"canonical_record":{"source":{"id":"1810.04790","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-10-10T03:16:01Z","cross_cats_sorted":[],"title_canon_sha256":"d2e423b3520e7bbf580938b05e8c35e915b2f661ca029b0318bb2f5e293d6170","abstract_canon_sha256":"7e75283e6aeba2d8779889907424be3d2bea92696e796c1d71a73879b964e0da"},"schema_version":"1.0"},"canonical_sha256":"6c6eec71bc203baaa18ba6051f35858e1440b8ecdb34cc527219a842e6088707","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:35.879726Z","signature_b64":"KKZgnXvlxTxZAWkBSOwQ7JoQ3uineEdvbRCHLc7djBBjjAndl9i7463QSkpFuw5NCdL1mT+YQFy78kQ9Qn7vCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c6eec71bc203baaa18ba6051f35858e1440b8ecdb34cc527219a842e6088707","last_reissued_at":"2026-05-18T00:03:35.879128Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:35.879128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.04790","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":"2026-05-18T00:03:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rBUiR0+m83lh2iCf8vU4v9RORWug0FGEXVppFK1/guuLesu9K6bjyMD/st9lxN1w4KXqUhY9Icmm9jmWSsZtDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T07:49:03.904546Z"},"content_sha256":"9c2076a1815a42d9f137b454f55a6c329cbd92e0b3a0e6a70e315183b25d02cf","schema_version":"1.0","event_id":"sha256:9c2076a1815a42d9f137b454f55a6c329cbd92e0b3a0e6a70e315183b25d02cf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:NRXOY4N4EA52VIMLUYCR6NMFRY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Trace functions of the Parafermion vertex operator algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Chongying Dong, Li Ren, Victor G. Kac","submitted_at":"2018-10-10T03:16:01Z","abstract_excerpt":"The trace functions for the Parafermion vertex operator algebra associated to any finite dimensional simple Lie algebra $\\g$ and any positive integer $k$ are studied and an explicit modular transformation formula of the trace functions is obtained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04790","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":"2026-05-18T00:03:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rDK5HBTnkBzV5jcuHNCYsxNkFxbHVhFW0RyJLHiubD3D4rmjHDuyTn0T31VrfYgFIZmQ2EivucEKS1ZIKAcVBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T07:49:03.904884Z"},"content_sha256":"f2cb9aa2fb2dbc0cc90196bfcfc897d8391ade028b638b98175701d7f47ee247","schema_version":"1.0","event_id":"sha256:f2cb9aa2fb2dbc0cc90196bfcfc897d8391ade028b638b98175701d7f47ee247"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NRXOY4N4EA52VIMLUYCR6NMFRY/bundle.json","state_url":"https://pith.science/pith/NRXOY4N4EA52VIMLUYCR6NMFRY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NRXOY4N4EA52VIMLUYCR6NMFRY/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":"2026-06-03T07:49:03Z","links":{"resolver":"https://pith.science/pith/NRXOY4N4EA52VIMLUYCR6NMFRY","bundle":"https://pith.science/pith/NRXOY4N4EA52VIMLUYCR6NMFRY/bundle.json","state":"https://pith.science/pith/NRXOY4N4EA52VIMLUYCR6NMFRY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NRXOY4N4EA52VIMLUYCR6NMFRY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:NRXOY4N4EA52VIMLUYCR6NMFRY","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":"7e75283e6aeba2d8779889907424be3d2bea92696e796c1d71a73879b964e0da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-10-10T03:16:01Z","title_canon_sha256":"d2e423b3520e7bbf580938b05e8c35e915b2f661ca029b0318bb2f5e293d6170"},"schema_version":"1.0","source":{"id":"1810.04790","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.04790","created_at":"2026-05-18T00:03:35Z"},{"alias_kind":"arxiv_version","alias_value":"1810.04790v1","created_at":"2026-05-18T00:03:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.04790","created_at":"2026-05-18T00:03:35Z"},{"alias_kind":"pith_short_12","alias_value":"NRXOY4N4EA52","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NRXOY4N4EA52VIML","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NRXOY4N4","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:f2cb9aa2fb2dbc0cc90196bfcfc897d8391ade028b638b98175701d7f47ee247","target":"graph","created_at":"2026-05-18T00:03:35Z","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":"The trace functions for the Parafermion vertex operator algebra associated to any finite dimensional simple Lie algebra $\\g$ and any positive integer $k$ are studied and an explicit modular transformation formula of the trace functions is obtained.","authors_text":"Chongying Dong, Li Ren, Victor G. Kac","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-10-10T03:16:01Z","title":"Trace functions of the Parafermion vertex operator algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04790","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":"sha256:9c2076a1815a42d9f137b454f55a6c329cbd92e0b3a0e6a70e315183b25d02cf","target":"record","created_at":"2026-05-18T00:03:35Z","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":"7e75283e6aeba2d8779889907424be3d2bea92696e796c1d71a73879b964e0da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-10-10T03:16:01Z","title_canon_sha256":"d2e423b3520e7bbf580938b05e8c35e915b2f661ca029b0318bb2f5e293d6170"},"schema_version":"1.0","source":{"id":"1810.04790","kind":"arxiv","version":1}},"canonical_sha256":"6c6eec71bc203baaa18ba6051f35858e1440b8ecdb34cc527219a842e6088707","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c6eec71bc203baaa18ba6051f35858e1440b8ecdb34cc527219a842e6088707","first_computed_at":"2026-05-18T00:03:35.879128Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:35.879128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KKZgnXvlxTxZAWkBSOwQ7JoQ3uineEdvbRCHLc7djBBjjAndl9i7463QSkpFuw5NCdL1mT+YQFy78kQ9Qn7vCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:35.879726Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.04790","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c2076a1815a42d9f137b454f55a6c329cbd92e0b3a0e6a70e315183b25d02cf","sha256:f2cb9aa2fb2dbc0cc90196bfcfc897d8391ade028b638b98175701d7f47ee247"],"state_sha256":"a9cc527ad19f534d3243ea9dd5afd9907d7fe3e3ba91029773a8a264796ccf63"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"21r2NWO2GUr5Z9bE3OI3Rp/JfDPBoy1bibFC0fuFRQidRJPNT15eSWdL3AB1sdeXcZrWe97qdhnsw0RYVP3dDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T07:49:03.906761Z","bundle_sha256":"eff77e1944f465a47b9d3fb046b9b8b6369a322965df82a07ddef3c5d3aa6b7b"}}