{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:6N7YD52ZRW5GML2BEOTFK3B4SH","short_pith_number":"pith:6N7YD52Z","canonical_record":{"source":{"id":"1311.2116","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-11-09T00:57:20Z","cross_cats_sorted":["math-ph","math.MP","math.QA"],"title_canon_sha256":"0c49bc21596cbdaa37563d282bc5b4c29b9c68ed63a42fb0f5cb37921a44c82e","abstract_canon_sha256":"c172fc676566c32c2c7a281d5f6b1cdae5a743a5b4f25230abef28564adfb35e"},"schema_version":"1.0"},"canonical_sha256":"f37f81f7598dba662f4123a6556c3c91e57a0d1d1450adf79c426aee9a918d74","source":{"kind":"arxiv","id":"1311.2116","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.2116","created_at":"2026-05-18T03:07:03Z"},{"alias_kind":"arxiv_version","alias_value":"1311.2116v2","created_at":"2026-05-18T03:07:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.2116","created_at":"2026-05-18T03:07:03Z"},{"alias_kind":"pith_short_12","alias_value":"6N7YD52ZRW5G","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6N7YD52ZRW5GML2B","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6N7YD52Z","created_at":"2026-05-18T12:27:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:6N7YD52ZRW5GML2BEOTFK3B4SH","target":"record","payload":{"canonical_record":{"source":{"id":"1311.2116","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-11-09T00:57:20Z","cross_cats_sorted":["math-ph","math.MP","math.QA"],"title_canon_sha256":"0c49bc21596cbdaa37563d282bc5b4c29b9c68ed63a42fb0f5cb37921a44c82e","abstract_canon_sha256":"c172fc676566c32c2c7a281d5f6b1cdae5a743a5b4f25230abef28564adfb35e"},"schema_version":"1.0"},"canonical_sha256":"f37f81f7598dba662f4123a6556c3c91e57a0d1d1450adf79c426aee9a918d74","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:03.427351Z","signature_b64":"sO7JGh7zESXNwI1AUljhyR9lqFTZzhS37L9Q+l7FcpYs+u0b7esm2P/pYWCsaFgnktGrHHanSb1yBWpRRbzmBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f37f81f7598dba662f4123a6556c3c91e57a0d1d1450adf79c426aee9a918d74","last_reissued_at":"2026-05-18T03:07:03.426790Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:03.426790Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.2116","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:07:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KjsE6upwgCQqaM9h0yaRo5x0HO7ZaYLbbwWuoP7Ut0vZ2NMLWiNy1P3VjpEGQHHHQONnsSEnE5isbSDplLEbBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T12:50:02.057346Z"},"content_sha256":"db780ffdeffc1dcb43ef55bf142912f5c47340c6dccde27684c7b38f37166ba1","schema_version":"1.0","event_id":"sha256:db780ffdeffc1dcb43ef55bf142912f5c47340c6dccde27684c7b38f37166ba1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:6N7YD52ZRW5GML2BEOTFK3B4SH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Characterizations of the exceptional vertex operator algebras of central charge $1$: II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.QA"],"primary_cat":"math.RT","authors_text":"Xianzu Lin","submitted_at":"2013-11-09T00:57:20Z","abstract_excerpt":"It is the second paper in a series devoted to the investigation of characterizations of the exceptional vertex operator algebras of central charge 1. In this paper, we give a characterization of the rational vertex operator algebra VOL, where L is the root lattice of type A1 and O is the octahedral group."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.2116","kind":"arxiv","version":2},"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":"2026-05-18T03:07:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8LX+bsEkz4AoPORxdq6soeTxX4S6Qbs3du2bk3IRMm8kpjIysJXofqe8k58HT1oh0pOSRveB+qZW7hJjd6IyDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T12:50:02.057704Z"},"content_sha256":"87debf2fe8d606ab6b8264eacdf534eae66383a9122c5c3d1e26ba4605e4eaaa","schema_version":"1.0","event_id":"sha256:87debf2fe8d606ab6b8264eacdf534eae66383a9122c5c3d1e26ba4605e4eaaa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6N7YD52ZRW5GML2BEOTFK3B4SH/bundle.json","state_url":"https://pith.science/pith/6N7YD52ZRW5GML2BEOTFK3B4SH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6N7YD52ZRW5GML2BEOTFK3B4SH/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":"2026-06-05T12:50:02Z","links":{"resolver":"https://pith.science/pith/6N7YD52ZRW5GML2BEOTFK3B4SH","bundle":"https://pith.science/pith/6N7YD52ZRW5GML2BEOTFK3B4SH/bundle.json","state":"https://pith.science/pith/6N7YD52ZRW5GML2BEOTFK3B4SH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6N7YD52ZRW5GML2BEOTFK3B4SH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:6N7YD52ZRW5GML2BEOTFK3B4SH","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":"c172fc676566c32c2c7a281d5f6b1cdae5a743a5b4f25230abef28564adfb35e","cross_cats_sorted":["math-ph","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-11-09T00:57:20Z","title_canon_sha256":"0c49bc21596cbdaa37563d282bc5b4c29b9c68ed63a42fb0f5cb37921a44c82e"},"schema_version":"1.0","source":{"id":"1311.2116","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.2116","created_at":"2026-05-18T03:07:03Z"},{"alias_kind":"arxiv_version","alias_value":"1311.2116v2","created_at":"2026-05-18T03:07:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.2116","created_at":"2026-05-18T03:07:03Z"},{"alias_kind":"pith_short_12","alias_value":"6N7YD52ZRW5G","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6N7YD52ZRW5GML2B","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6N7YD52Z","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:87debf2fe8d606ab6b8264eacdf534eae66383a9122c5c3d1e26ba4605e4eaaa","target":"graph","created_at":"2026-05-18T03:07:03Z","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":"It is the second paper in a series devoted to the investigation of characterizations of the exceptional vertex operator algebras of central charge 1. In this paper, we give a characterization of the rational vertex operator algebra VOL, where L is the root lattice of type A1 and O is the octahedral group.","authors_text":"Xianzu Lin","cross_cats":["math-ph","math.MP","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-11-09T00:57:20Z","title":"Characterizations of the exceptional vertex operator algebras of central charge $1$: II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.2116","kind":"arxiv","version":2},"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:db780ffdeffc1dcb43ef55bf142912f5c47340c6dccde27684c7b38f37166ba1","target":"record","created_at":"2026-05-18T03:07:03Z","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":"c172fc676566c32c2c7a281d5f6b1cdae5a743a5b4f25230abef28564adfb35e","cross_cats_sorted":["math-ph","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-11-09T00:57:20Z","title_canon_sha256":"0c49bc21596cbdaa37563d282bc5b4c29b9c68ed63a42fb0f5cb37921a44c82e"},"schema_version":"1.0","source":{"id":"1311.2116","kind":"arxiv","version":2}},"canonical_sha256":"f37f81f7598dba662f4123a6556c3c91e57a0d1d1450adf79c426aee9a918d74","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f37f81f7598dba662f4123a6556c3c91e57a0d1d1450adf79c426aee9a918d74","first_computed_at":"2026-05-18T03:07:03.426790Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:03.426790Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sO7JGh7zESXNwI1AUljhyR9lqFTZzhS37L9Q+l7FcpYs+u0b7esm2P/pYWCsaFgnktGrHHanSb1yBWpRRbzmBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:03.427351Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.2116","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db780ffdeffc1dcb43ef55bf142912f5c47340c6dccde27684c7b38f37166ba1","sha256:87debf2fe8d606ab6b8264eacdf534eae66383a9122c5c3d1e26ba4605e4eaaa"],"state_sha256":"3bd9ba9425ee3f9cf05587b452489a0d7a5bb5e960084e162cbd4b5c928f398e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ANZ47GwFlBCOHUqmJRLQfhELv/Y6I1djnumh9dIb5bCPn/hRKNxNd/H5fZMYfLkSiI0KuiAsSUUV3D3eBj8mAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T12:50:02.059700Z","bundle_sha256":"f122e57c4cb0d98b6c02c2d22e3d98d934f430e399ede47261a0445493ff40f8"}}