{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:GCWGA5ZS6CO67VPVQ5BR56WV53","short_pith_number":"pith:GCWGA5ZS","canonical_record":{"source":{"id":"1508.06940","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-08-27T16:58:15Z","cross_cats_sorted":[],"title_canon_sha256":"bbac555fb38a1ed037702e87333c8e14a8aa50025d45cc54d125efa70f95bc57","abstract_canon_sha256":"50a5acb19c073abde251b8fe2dfba460cb13933200e691f5c11254c8ec14779b"},"schema_version":"1.0"},"canonical_sha256":"30ac607732f09defd5f587431efad5eecc2c6d4589992b33c9114d03eac9eda4","source":{"kind":"arxiv","id":"1508.06940","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.06940","created_at":"2026-05-18T00:30:28Z"},{"alias_kind":"arxiv_version","alias_value":"1508.06940v1","created_at":"2026-05-18T00:30:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.06940","created_at":"2026-05-18T00:30:28Z"},{"alias_kind":"pith_short_12","alias_value":"GCWGA5ZS6CO6","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GCWGA5ZS6CO67VPV","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GCWGA5ZS","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:GCWGA5ZS6CO67VPVQ5BR56WV53","target":"record","payload":{"canonical_record":{"source":{"id":"1508.06940","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-08-27T16:58:15Z","cross_cats_sorted":[],"title_canon_sha256":"bbac555fb38a1ed037702e87333c8e14a8aa50025d45cc54d125efa70f95bc57","abstract_canon_sha256":"50a5acb19c073abde251b8fe2dfba460cb13933200e691f5c11254c8ec14779b"},"schema_version":"1.0"},"canonical_sha256":"30ac607732f09defd5f587431efad5eecc2c6d4589992b33c9114d03eac9eda4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:28.952723Z","signature_b64":"iJqRO8NKSse+LooAplJV2Zact78QcEGk8pOGIsarsppaTJ5zo4BrijTGFR+U1Qa/3Am9HKo9Kfa7C26hZ5XQDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"30ac607732f09defd5f587431efad5eecc2c6d4589992b33c9114d03eac9eda4","last_reissued_at":"2026-05-18T00:30:28.952101Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:28.952101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.06940","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":"2026-05-18T00:30:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x+xnanq25+j7bdGnRYwdKbonFjwvtSu8zk6+g0OkiOSKCE0NumWmU0FY4ElyDB57w31unFliWaI6AUzbSsVGAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T18:38:35.804034Z"},"content_sha256":"10c30d76861d77dc57af45352d9e92fd92a0c740243ca90a9b098e1793ccaf66","schema_version":"1.0","event_id":"sha256:10c30d76861d77dc57af45352d9e92fd92a0c740243ca90a9b098e1793ccaf66"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:GCWGA5ZS6CO67VPVQ5BR56WV53","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Do $n$-Lie algebras have universal enveloping algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Rustam Turdibaev, Tim Van der Linden, Xabier Garcia-Martinez","submitted_at":"2015-08-27T16:58:15Z","abstract_excerpt":"The aim of this paper is to investigate in which sense, for $n\\geq 3$, $n$-Lie algebras admit universal enveloping algebras. There have been some attempts at a construction (see [10] and [5]) but after analysing those we come to the conclusion that they cannot be valid in general. We give counterexamples and sufficient conditions.\n  We then study the problem in its full generality, showing that universality is incompatible with the wish that the category of modules over a given $n$-Lie algebra $L$ is equivalent to the category of modules over the associated algebra $U(L)$. Indeed, an associate"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06940","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":"2026-05-18T00:30:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A8Tmir4YBdEiEHx24W0iU5OZ5FXsFdGOy4urOKLbbZf7a6RAz41GmASlIeJbcp4SfVY41w11NigVINZ3gsXyAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T18:38:35.804706Z"},"content_sha256":"ffe1c34031786d0dc58801ac8af876f5eae0b8d24463bc64d228e7c4775ed28d","schema_version":"1.0","event_id":"sha256:ffe1c34031786d0dc58801ac8af876f5eae0b8d24463bc64d228e7c4775ed28d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GCWGA5ZS6CO67VPVQ5BR56WV53/bundle.json","state_url":"https://pith.science/pith/GCWGA5ZS6CO67VPVQ5BR56WV53/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GCWGA5ZS6CO67VPVQ5BR56WV53/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":"2026-06-09T18:38:35Z","links":{"resolver":"https://pith.science/pith/GCWGA5ZS6CO67VPVQ5BR56WV53","bundle":"https://pith.science/pith/GCWGA5ZS6CO67VPVQ5BR56WV53/bundle.json","state":"https://pith.science/pith/GCWGA5ZS6CO67VPVQ5BR56WV53/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GCWGA5ZS6CO67VPVQ5BR56WV53/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GCWGA5ZS6CO67VPVQ5BR56WV53","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":"50a5acb19c073abde251b8fe2dfba460cb13933200e691f5c11254c8ec14779b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-08-27T16:58:15Z","title_canon_sha256":"bbac555fb38a1ed037702e87333c8e14a8aa50025d45cc54d125efa70f95bc57"},"schema_version":"1.0","source":{"id":"1508.06940","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.06940","created_at":"2026-05-18T00:30:28Z"},{"alias_kind":"arxiv_version","alias_value":"1508.06940v1","created_at":"2026-05-18T00:30:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.06940","created_at":"2026-05-18T00:30:28Z"},{"alias_kind":"pith_short_12","alias_value":"GCWGA5ZS6CO6","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GCWGA5ZS6CO67VPV","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GCWGA5ZS","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:ffe1c34031786d0dc58801ac8af876f5eae0b8d24463bc64d228e7c4775ed28d","target":"graph","created_at":"2026-05-18T00:30:28Z","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 aim of this paper is to investigate in which sense, for $n\\geq 3$, $n$-Lie algebras admit universal enveloping algebras. There have been some attempts at a construction (see [10] and [5]) but after analysing those we come to the conclusion that they cannot be valid in general. We give counterexamples and sufficient conditions.\n  We then study the problem in its full generality, showing that universality is incompatible with the wish that the category of modules over a given $n$-Lie algebra $L$ is equivalent to the category of modules over the associated algebra $U(L)$. Indeed, an associate","authors_text":"Rustam Turdibaev, Tim Van der Linden, Xabier Garcia-Martinez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-08-27T16:58:15Z","title":"Do $n$-Lie algebras have universal enveloping algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06940","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":"sha256:10c30d76861d77dc57af45352d9e92fd92a0c740243ca90a9b098e1793ccaf66","target":"record","created_at":"2026-05-18T00:30:28Z","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":"50a5acb19c073abde251b8fe2dfba460cb13933200e691f5c11254c8ec14779b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-08-27T16:58:15Z","title_canon_sha256":"bbac555fb38a1ed037702e87333c8e14a8aa50025d45cc54d125efa70f95bc57"},"schema_version":"1.0","source":{"id":"1508.06940","kind":"arxiv","version":1}},"canonical_sha256":"30ac607732f09defd5f587431efad5eecc2c6d4589992b33c9114d03eac9eda4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"30ac607732f09defd5f587431efad5eecc2c6d4589992b33c9114d03eac9eda4","first_computed_at":"2026-05-18T00:30:28.952101Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:28.952101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iJqRO8NKSse+LooAplJV2Zact78QcEGk8pOGIsarsppaTJ5zo4BrijTGFR+U1Qa/3Am9HKo9Kfa7C26hZ5XQDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:28.952723Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.06940","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:10c30d76861d77dc57af45352d9e92fd92a0c740243ca90a9b098e1793ccaf66","sha256:ffe1c34031786d0dc58801ac8af876f5eae0b8d24463bc64d228e7c4775ed28d"],"state_sha256":"724b91f4c56c5cf546900c0094abb79eed452489e5d5fb5103d042e65faf366e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lzJrVgGkxxuBkwL0+/Bq560UG63YvkknsFJrRip9NiLBrFEwJ6uEcXjoHSzwn16irk2tNv4EfFA4hPOFgbcDDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T18:38:35.808614Z","bundle_sha256":"dd699b18c357f892b4a5d1c66e55add8671d9258e40ef016373a197bcba5f4ee"}}