{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:EYBAU7OX6VSTHOAO2ERBOFD7HS","short_pith_number":"pith:EYBAU7OX","canonical_record":{"source":{"id":"1611.07655","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-11-23T06:24:07Z","cross_cats_sorted":[],"title_canon_sha256":"301e8521f1fed34ef33cbefbfcc9604f8b90d9c355c5aa3071f3747cc3e13ecd","abstract_canon_sha256":"f9def4e0e20c29fe724f00b8e65e5f7b74c8706c7a3ec6446d607282901d972f"},"schema_version":"1.0"},"canonical_sha256":"26020a7dd7f56533b80ed12217147f3c8a786cf59ba90199939fbf0142bd8e31","source":{"kind":"arxiv","id":"1611.07655","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.07655","created_at":"2026-05-18T00:53:24Z"},{"alias_kind":"arxiv_version","alias_value":"1611.07655v2","created_at":"2026-05-18T00:53:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.07655","created_at":"2026-05-18T00:53:24Z"},{"alias_kind":"pith_short_12","alias_value":"EYBAU7OX6VST","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"EYBAU7OX6VSTHOAO","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"EYBAU7OX","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:EYBAU7OX6VSTHOAO2ERBOFD7HS","target":"record","payload":{"canonical_record":{"source":{"id":"1611.07655","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-11-23T06:24:07Z","cross_cats_sorted":[],"title_canon_sha256":"301e8521f1fed34ef33cbefbfcc9604f8b90d9c355c5aa3071f3747cc3e13ecd","abstract_canon_sha256":"f9def4e0e20c29fe724f00b8e65e5f7b74c8706c7a3ec6446d607282901d972f"},"schema_version":"1.0"},"canonical_sha256":"26020a7dd7f56533b80ed12217147f3c8a786cf59ba90199939fbf0142bd8e31","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:24.009042Z","signature_b64":"dE9Ac7XPipSHUIopeLRs4OaeCQlMVfC9FTadjFkfhYpQqMsMSgksd9B8Ge/Bktxq6ZaYWrmvrFdhSlqWp5htAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26020a7dd7f56533b80ed12217147f3c8a786cf59ba90199939fbf0142bd8e31","last_reissued_at":"2026-05-18T00:53:24.008568Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:24.008568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.07655","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":"2026-05-18T00:53:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AZGy9P6lFB8m3DF2oE/MemEArS/fBbMiwhWpb15o5F/ec31h3DbhY1gFpZ7Zz0PpqOXSDQHmIHuDEgzc4IqEAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:32:04.456057Z"},"content_sha256":"43a54d642bd9fbe0ddbee527459ba793f39b569f7e3e1b6bda2f7a3000e8e767","schema_version":"1.0","event_id":"sha256:43a54d642bd9fbe0ddbee527459ba793f39b569f7e3e1b6bda2f7a3000e8e767"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:EYBAU7OX6VSTHOAO2ERBOFD7HS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$\\mathbb{Z}_2$-orbifold construction associated with $(-1)$-isometry and uniqueness of holomorphic vertex operator algebras of central charge 24","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Ching Hung Lam, Kazuya Kawasetsu, Xingjun Lin","submitted_at":"2016-11-23T06:24:07Z","abstract_excerpt":"The vertex operator algebra structure of a strongly regular holomorphic vertex operator algebra $V$ of central charge $24$ is proved to be uniquely determined by the Lie algebra structure of its weight one space $V_1$ if $V_1$ is a Lie algebra of the type $A_{1,4}^{12}$, $B_{2,2}^6$, $B_{3,2}^4$, $B_{4,2}^3$, $B_{6,2}^2$, $B_{12,2}$, $D_{4,2}^2B_{2,1}^4$, $D_{8,2}B_{4,1}^2$, $A_{3,2}^4A_{1,1}^4$, $D_{5,2}^2A_{3,1}^2$, $D_{9,2}A_{7,1}$, $C_{4,1}^4$ or $D_{6,2}B_{3,1}^2C_{4,1}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07655","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":"2026-05-18T00:53:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v7DI2PxV5gwIV5cCWk3mq6+fGJNgkiJiQf8tvfnADIdkx26ysghvB2S2i289Beo+1JdvNSHl2UFq0+WnP4PcBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:32:04.456764Z"},"content_sha256":"49e0ac4b42e8d32d2a7f802e63bf6c0b737ecc18a0e5b4cf894a282ff2976c1d","schema_version":"1.0","event_id":"sha256:49e0ac4b42e8d32d2a7f802e63bf6c0b737ecc18a0e5b4cf894a282ff2976c1d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EYBAU7OX6VSTHOAO2ERBOFD7HS/bundle.json","state_url":"https://pith.science/pith/EYBAU7OX6VSTHOAO2ERBOFD7HS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EYBAU7OX6VSTHOAO2ERBOFD7HS/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":"2026-05-31T23:32:04Z","links":{"resolver":"https://pith.science/pith/EYBAU7OX6VSTHOAO2ERBOFD7HS","bundle":"https://pith.science/pith/EYBAU7OX6VSTHOAO2ERBOFD7HS/bundle.json","state":"https://pith.science/pith/EYBAU7OX6VSTHOAO2ERBOFD7HS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EYBAU7OX6VSTHOAO2ERBOFD7HS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:EYBAU7OX6VSTHOAO2ERBOFD7HS","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":"f9def4e0e20c29fe724f00b8e65e5f7b74c8706c7a3ec6446d607282901d972f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-11-23T06:24:07Z","title_canon_sha256":"301e8521f1fed34ef33cbefbfcc9604f8b90d9c355c5aa3071f3747cc3e13ecd"},"schema_version":"1.0","source":{"id":"1611.07655","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.07655","created_at":"2026-05-18T00:53:24Z"},{"alias_kind":"arxiv_version","alias_value":"1611.07655v2","created_at":"2026-05-18T00:53:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.07655","created_at":"2026-05-18T00:53:24Z"},{"alias_kind":"pith_short_12","alias_value":"EYBAU7OX6VST","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"EYBAU7OX6VSTHOAO","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"EYBAU7OX","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:49e0ac4b42e8d32d2a7f802e63bf6c0b737ecc18a0e5b4cf894a282ff2976c1d","target":"graph","created_at":"2026-05-18T00:53:24Z","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 vertex operator algebra structure of a strongly regular holomorphic vertex operator algebra $V$ of central charge $24$ is proved to be uniquely determined by the Lie algebra structure of its weight one space $V_1$ if $V_1$ is a Lie algebra of the type $A_{1,4}^{12}$, $B_{2,2}^6$, $B_{3,2}^4$, $B_{4,2}^3$, $B_{6,2}^2$, $B_{12,2}$, $D_{4,2}^2B_{2,1}^4$, $D_{8,2}B_{4,1}^2$, $A_{3,2}^4A_{1,1}^4$, $D_{5,2}^2A_{3,1}^2$, $D_{9,2}A_{7,1}$, $C_{4,1}^4$ or $D_{6,2}B_{3,1}^2C_{4,1}$.","authors_text":"Ching Hung Lam, Kazuya Kawasetsu, Xingjun Lin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-11-23T06:24:07Z","title":"$\\mathbb{Z}_2$-orbifold construction associated with $(-1)$-isometry and uniqueness of holomorphic vertex operator algebras of central charge 24"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07655","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":"sha256:43a54d642bd9fbe0ddbee527459ba793f39b569f7e3e1b6bda2f7a3000e8e767","target":"record","created_at":"2026-05-18T00:53:24Z","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":"f9def4e0e20c29fe724f00b8e65e5f7b74c8706c7a3ec6446d607282901d972f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-11-23T06:24:07Z","title_canon_sha256":"301e8521f1fed34ef33cbefbfcc9604f8b90d9c355c5aa3071f3747cc3e13ecd"},"schema_version":"1.0","source":{"id":"1611.07655","kind":"arxiv","version":2}},"canonical_sha256":"26020a7dd7f56533b80ed12217147f3c8a786cf59ba90199939fbf0142bd8e31","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26020a7dd7f56533b80ed12217147f3c8a786cf59ba90199939fbf0142bd8e31","first_computed_at":"2026-05-18T00:53:24.008568Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:24.008568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dE9Ac7XPipSHUIopeLRs4OaeCQlMVfC9FTadjFkfhYpQqMsMSgksd9B8Ge/Bktxq6ZaYWrmvrFdhSlqWp5htAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:24.009042Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.07655","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43a54d642bd9fbe0ddbee527459ba793f39b569f7e3e1b6bda2f7a3000e8e767","sha256:49e0ac4b42e8d32d2a7f802e63bf6c0b737ecc18a0e5b4cf894a282ff2976c1d"],"state_sha256":"0c7538d51f802b0d421c865887d23d0fa0cb0fd2902fc6ebe4a4a0877c7ee08b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jz9+LwTdkB57S90R7Gg/D4LelCeVDz2Ts3oIn7QNHGnsVj7+EYXk/kuuaKjz/9ZljR0saci3va7sJlwd7SLWAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T23:32:04.460743Z","bundle_sha256":"17ad2716d901ac09c4f4de8c5145fcfed94436b18edb0bf635089dee3375d3f8"}}