{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:GYCOV46OUNIOLPQZCCG4S44YD4","short_pith_number":"pith:GYCOV46O","canonical_record":{"source":{"id":"1902.05741","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-02-15T09:41:24Z","cross_cats_sorted":["math.MP","math.RT"],"title_canon_sha256":"a7f16793137f6c1e5988173b199923e66274d23342cf27415692fcf3d6dd1d08","abstract_canon_sha256":"bb61b0a48d2458bbab09a97e71ba855c95932a8ba20ebdc531132604e70559c8"},"schema_version":"1.0"},"canonical_sha256":"3604eaf3cea350e5be19108dc973981f19e481926b48a93069dc3e0ff09d3b48","source":{"kind":"arxiv","id":"1902.05741","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.05741","created_at":"2026-07-05T01:17:06Z"},{"alias_kind":"arxiv_version","alias_value":"1902.05741v2","created_at":"2026-07-05T01:17:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.05741","created_at":"2026-07-05T01:17:06Z"},{"alias_kind":"pith_short_12","alias_value":"GYCOV46OUNIO","created_at":"2026-07-05T01:17:06Z"},{"alias_kind":"pith_short_16","alias_value":"GYCOV46OUNIOLPQZ","created_at":"2026-07-05T01:17:06Z"},{"alias_kind":"pith_short_8","alias_value":"GYCOV46O","created_at":"2026-07-05T01:17:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:GYCOV46OUNIOLPQZCCG4S44YD4","target":"record","payload":{"canonical_record":{"source":{"id":"1902.05741","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-02-15T09:41:24Z","cross_cats_sorted":["math.MP","math.RT"],"title_canon_sha256":"a7f16793137f6c1e5988173b199923e66274d23342cf27415692fcf3d6dd1d08","abstract_canon_sha256":"bb61b0a48d2458bbab09a97e71ba855c95932a8ba20ebdc531132604e70559c8"},"schema_version":"1.0"},"canonical_sha256":"3604eaf3cea350e5be19108dc973981f19e481926b48a93069dc3e0ff09d3b48","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:17:06.106978Z","signature_b64":"bC48BS4CuQU6Oev7UVVvI0KXpsE0G37lBauYRZufMhioAoJ44/AIfhX4Vol1lHnN6d/eR+C8lyqD3Z9DNS9tCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3604eaf3cea350e5be19108dc973981f19e481926b48a93069dc3e0ff09d3b48","last_reissued_at":"2026-07-05T01:17:06.106359Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:17:06.106359Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.05741","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":"2026-07-05T01:17:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lg5y9tp//615VbyVPH6BxbBkWtGCZ4A+DWZ6rdxp/xypMbJkhCSlo8cU7XEymQXvWGFL8VsjuzUcWz7+B5JHBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T04:35:10.598718Z"},"content_sha256":"6a325db3b29f0600521bd7e3a738e0931d22c873db17e30f79dfe90d7573aab4","schema_version":"1.0","event_id":"sha256:6a325db3b29f0600521bd7e3a738e0931d22c873db17e30f79dfe90d7573aab4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:GYCOV46OUNIOLPQZCCG4S44YD4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$\\mathbb{Z}_2 \\times \\mathbb{Z}_2$ generalizations of infinite dimensional Lie superalgebra of conformal type with complete classification of central extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.RT"],"primary_cat":"math-ph","authors_text":"J. Segar, N. Aizawa, P. S. Isaac","submitted_at":"2019-02-15T09:41:24Z","abstract_excerpt":"We introduce a class of novel $\\mathbb{Z}_2 \\times \\mathbb{Z}_2$-graded color superalgebras of infinite dimension. It is done by realizing each member of the class in the universal enveloping algebra of a Lie superalgebra which is a module extension of the Virasoro algebra. Then the complete classification of central extensions of the $\\mathbb{Z}_2 \\times \\mathbb{Z}_2$-graded color superalgebras is presented. It turns out that infinitely many members of the class have non-trivial extensions. We also demonstrate that the color superalgebras (with and without central extensions) have adjoint and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.05741","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1902.05741/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T01:17:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HqBl0/GhTc1WzDQIxzYoHJBsoYxz8k/kfUfnsiCOADbJFKZ8CqYY0K65uIbJojr2puy09uZiwm7LJp9Jo43lDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T04:35:10.599084Z"},"content_sha256":"ce9fe4052e0c3904c19204d9b1bfdeb8d5973d5a96dee0868f49bbc6cd460c94","schema_version":"1.0","event_id":"sha256:ce9fe4052e0c3904c19204d9b1bfdeb8d5973d5a96dee0868f49bbc6cd460c94"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GYCOV46OUNIOLPQZCCG4S44YD4/bundle.json","state_url":"https://pith.science/pith/GYCOV46OUNIOLPQZCCG4S44YD4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GYCOV46OUNIOLPQZCCG4S44YD4/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":"2026-07-05T04:35:10Z","links":{"resolver":"https://pith.science/pith/GYCOV46OUNIOLPQZCCG4S44YD4","bundle":"https://pith.science/pith/GYCOV46OUNIOLPQZCCG4S44YD4/bundle.json","state":"https://pith.science/pith/GYCOV46OUNIOLPQZCCG4S44YD4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GYCOV46OUNIOLPQZCCG4S44YD4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:GYCOV46OUNIOLPQZCCG4S44YD4","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":"bb61b0a48d2458bbab09a97e71ba855c95932a8ba20ebdc531132604e70559c8","cross_cats_sorted":["math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-02-15T09:41:24Z","title_canon_sha256":"a7f16793137f6c1e5988173b199923e66274d23342cf27415692fcf3d6dd1d08"},"schema_version":"1.0","source":{"id":"1902.05741","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.05741","created_at":"2026-07-05T01:17:06Z"},{"alias_kind":"arxiv_version","alias_value":"1902.05741v2","created_at":"2026-07-05T01:17:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.05741","created_at":"2026-07-05T01:17:06Z"},{"alias_kind":"pith_short_12","alias_value":"GYCOV46OUNIO","created_at":"2026-07-05T01:17:06Z"},{"alias_kind":"pith_short_16","alias_value":"GYCOV46OUNIOLPQZ","created_at":"2026-07-05T01:17:06Z"},{"alias_kind":"pith_short_8","alias_value":"GYCOV46O","created_at":"2026-07-05T01:17:06Z"}],"graph_snapshots":[{"event_id":"sha256:ce9fe4052e0c3904c19204d9b1bfdeb8d5973d5a96dee0868f49bbc6cd460c94","target":"graph","created_at":"2026-07-05T01:17:06Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1902.05741/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a class of novel $\\mathbb{Z}_2 \\times \\mathbb{Z}_2$-graded color superalgebras of infinite dimension. It is done by realizing each member of the class in the universal enveloping algebra of a Lie superalgebra which is a module extension of the Virasoro algebra. Then the complete classification of central extensions of the $\\mathbb{Z}_2 \\times \\mathbb{Z}_2$-graded color superalgebras is presented. It turns out that infinitely many members of the class have non-trivial extensions. We also demonstrate that the color superalgebras (with and without central extensions) have adjoint and","authors_text":"J. Segar, N. Aizawa, P. S. Isaac","cross_cats":["math.MP","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-02-15T09:41:24Z","title":"$\\mathbb{Z}_2 \\times \\mathbb{Z}_2$ generalizations of infinite dimensional Lie superalgebra of conformal type with complete classification of central extensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.05741","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":"sha256:6a325db3b29f0600521bd7e3a738e0931d22c873db17e30f79dfe90d7573aab4","target":"record","created_at":"2026-07-05T01:17:06Z","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":"bb61b0a48d2458bbab09a97e71ba855c95932a8ba20ebdc531132604e70559c8","cross_cats_sorted":["math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-02-15T09:41:24Z","title_canon_sha256":"a7f16793137f6c1e5988173b199923e66274d23342cf27415692fcf3d6dd1d08"},"schema_version":"1.0","source":{"id":"1902.05741","kind":"arxiv","version":2}},"canonical_sha256":"3604eaf3cea350e5be19108dc973981f19e481926b48a93069dc3e0ff09d3b48","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3604eaf3cea350e5be19108dc973981f19e481926b48a93069dc3e0ff09d3b48","first_computed_at":"2026-07-05T01:17:06.106359Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:17:06.106359Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bC48BS4CuQU6Oev7UVVvI0KXpsE0G37lBauYRZufMhioAoJ44/AIfhX4Vol1lHnN6d/eR+C8lyqD3Z9DNS9tCA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:17:06.106978Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.05741","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6a325db3b29f0600521bd7e3a738e0931d22c873db17e30f79dfe90d7573aab4","sha256:ce9fe4052e0c3904c19204d9b1bfdeb8d5973d5a96dee0868f49bbc6cd460c94"],"state_sha256":"cb9b57a85b6709458abcaab2b29f5b8cfd4a762c83cb0f2f80372a2169509840"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vC1g9nG0RDaRNRbT1vWw+f+RNz2rU9gZFlL3Jxkcb6hWOFOKKfAriu5486EqWASbgvRjtUN0I0D143AlSy4ZAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T04:35:10.601121Z","bundle_sha256":"a36cc65b7b201fb3a1897e9e8c50d4785c103669d6b2ab6442e15f97b5c6b0cf"}}