{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:XOEBVBQ6EUPVRQNYNHUE64IOYE","short_pith_number":"pith:XOEBVBQ6","canonical_record":{"source":{"id":"math/0307263","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2003-07-19T04:55:40Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"3b7774d2ef4bcfb727cb1e2249b4b5fc56404715d37a7419df38eed45318867c","abstract_canon_sha256":"c265e3765c706c39de45d6cc06dd313b44507b3a9d41341aa498875de6add4ad"},"schema_version":"1.0"},"canonical_sha256":"bb881a861e251f58c1b869e84f710ec12db40404066d252ab6aca1dc6c3b475c","source":{"kind":"arxiv","id":"math/0307263","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0307263","created_at":"2026-05-18T04:17:03Z"},{"alias_kind":"arxiv_version","alias_value":"math/0307263v6","created_at":"2026-05-18T04:17:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0307263","created_at":"2026-05-18T04:17:03Z"},{"alias_kind":"pith_short_12","alias_value":"XOEBVBQ6EUPV","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"XOEBVBQ6EUPVRQNY","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"XOEBVBQ6","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:XOEBVBQ6EUPVRQNYNHUE64IOYE","target":"record","payload":{"canonical_record":{"source":{"id":"math/0307263","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2003-07-19T04:55:40Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"3b7774d2ef4bcfb727cb1e2249b4b5fc56404715d37a7419df38eed45318867c","abstract_canon_sha256":"c265e3765c706c39de45d6cc06dd313b44507b3a9d41341aa498875de6add4ad"},"schema_version":"1.0"},"canonical_sha256":"bb881a861e251f58c1b869e84f710ec12db40404066d252ab6aca1dc6c3b475c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:17:03.704378Z","signature_b64":"oes32GBPhmA3drVeoTGxmsMBeOcKce+vTOgGD5fGxE9K7VP7y2LmmYV82/T2aaD+tJgCgRfJGyTLUCOrd/8iCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bb881a861e251f58c1b869e84f710ec12db40404066d252ab6aca1dc6c3b475c","last_reissued_at":"2026-05-18T04:17:03.703953Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:17:03.703953Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0307263","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:17:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BIAyi6YlZIMZFu/VOW4XKPaHn8bzy5lJ0ExHmWSpELRv1gzYzW1DV6RUMWYniIhuhMx9GRCIpzDgJ/U5PY4wAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T14:01:23.989687Z"},"content_sha256":"0a6786e55dd3840aee607e07149d823ad56e3fc3becb86bb40e67a6412306421","schema_version":"1.0","event_id":"sha256:0a6786e55dd3840aee607e07149d823ad56e3fc3becb86bb40e67a6412306421"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:XOEBVBQ6EUPVRQNYNHUE64IOYE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Higher-Dimensional Algebra VI: Lie 2-Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.QA","authors_text":"Alissa S. Crans, John C. Baez","submitted_at":"2003-07-19T04:55:40Z","abstract_excerpt":"The theory of Lie algebras can be categorified starting from a new notion of \"2-vector space\", which we define as an internal category in Vect. There is a 2-category 2Vect having these 2-vector spaces as objects, \"linear functors\" as morphisms and \"linear natural transformations\" as 2-morphisms. We define a \"semistrict Lie 2-algebra\" to be a 2-vector space L equipped with a skew-symmetric bilinear functor satisfying the Jacobi identity up to a completely antisymmetric trilinear natural transformation called the \"Jacobiator\", which in turn must satisfy a certain law of its own. This law is clos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0307263","kind":"arxiv","version":6},"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":"2026-05-18T04:17:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tDPf+SiUykujzVQI2qto9F+Fg80LeE4FBuQOa1DZ/DDAz96keGzjBk1s1K4WZM/lRvH07sGCiirBZBrwlOx9Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T14:01:23.990025Z"},"content_sha256":"85fe0642bf47a0250e52e0cc250cc294fd27424dba195865e3af0d5b0a5678c2","schema_version":"1.0","event_id":"sha256:85fe0642bf47a0250e52e0cc250cc294fd27424dba195865e3af0d5b0a5678c2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XOEBVBQ6EUPVRQNYNHUE64IOYE/bundle.json","state_url":"https://pith.science/pith/XOEBVBQ6EUPVRQNYNHUE64IOYE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XOEBVBQ6EUPVRQNYNHUE64IOYE/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":"2026-06-22T14:01:23Z","links":{"resolver":"https://pith.science/pith/XOEBVBQ6EUPVRQNYNHUE64IOYE","bundle":"https://pith.science/pith/XOEBVBQ6EUPVRQNYNHUE64IOYE/bundle.json","state":"https://pith.science/pith/XOEBVBQ6EUPVRQNYNHUE64IOYE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XOEBVBQ6EUPVRQNYNHUE64IOYE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:XOEBVBQ6EUPVRQNYNHUE64IOYE","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":"c265e3765c706c39de45d6cc06dd313b44507b3a9d41341aa498875de6add4ad","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2003-07-19T04:55:40Z","title_canon_sha256":"3b7774d2ef4bcfb727cb1e2249b4b5fc56404715d37a7419df38eed45318867c"},"schema_version":"1.0","source":{"id":"math/0307263","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0307263","created_at":"2026-05-18T04:17:03Z"},{"alias_kind":"arxiv_version","alias_value":"math/0307263v6","created_at":"2026-05-18T04:17:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0307263","created_at":"2026-05-18T04:17:03Z"},{"alias_kind":"pith_short_12","alias_value":"XOEBVBQ6EUPV","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"XOEBVBQ6EUPVRQNY","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"XOEBVBQ6","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:85fe0642bf47a0250e52e0cc250cc294fd27424dba195865e3af0d5b0a5678c2","target":"graph","created_at":"2026-05-18T04:17:03Z","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":"The theory of Lie algebras can be categorified starting from a new notion of \"2-vector space\", which we define as an internal category in Vect. There is a 2-category 2Vect having these 2-vector spaces as objects, \"linear functors\" as morphisms and \"linear natural transformations\" as 2-morphisms. We define a \"semistrict Lie 2-algebra\" to be a 2-vector space L equipped with a skew-symmetric bilinear functor satisfying the Jacobi identity up to a completely antisymmetric trilinear natural transformation called the \"Jacobiator\", which in turn must satisfy a certain law of its own. This law is clos","authors_text":"Alissa S. Crans, John C. Baez","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2003-07-19T04:55:40Z","title":"Higher-Dimensional Algebra VI: Lie 2-Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0307263","kind":"arxiv","version":6},"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":"sha256:0a6786e55dd3840aee607e07149d823ad56e3fc3becb86bb40e67a6412306421","target":"record","created_at":"2026-05-18T04:17:03Z","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":"c265e3765c706c39de45d6cc06dd313b44507b3a9d41341aa498875de6add4ad","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2003-07-19T04:55:40Z","title_canon_sha256":"3b7774d2ef4bcfb727cb1e2249b4b5fc56404715d37a7419df38eed45318867c"},"schema_version":"1.0","source":{"id":"math/0307263","kind":"arxiv","version":6}},"canonical_sha256":"bb881a861e251f58c1b869e84f710ec12db40404066d252ab6aca1dc6c3b475c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bb881a861e251f58c1b869e84f710ec12db40404066d252ab6aca1dc6c3b475c","first_computed_at":"2026-05-18T04:17:03.703953Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:17:03.703953Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oes32GBPhmA3drVeoTGxmsMBeOcKce+vTOgGD5fGxE9K7VP7y2LmmYV82/T2aaD+tJgCgRfJGyTLUCOrd/8iCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:17:03.704378Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0307263","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a6786e55dd3840aee607e07149d823ad56e3fc3becb86bb40e67a6412306421","sha256:85fe0642bf47a0250e52e0cc250cc294fd27424dba195865e3af0d5b0a5678c2"],"state_sha256":"ceff4d69a7ce6f7d017235a9f4d9006035721721e3a62900312df8829bbe7a45"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3vF2MZ2znc/ARkAyNamsS6EN1PORQ/viX41MjnbxI6m68EHrlG6LvS1HMZ9tYTMUP6tSJuxsga0l5NciNTTKCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T14:01:23.991984Z","bundle_sha256":"25cc47156149872a59b55eb12ec8c1aaedb61e046b8b88f2eeb44adeaf1e6850"}}