{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:NUGSQCLERRG5SZNBYCJQKFAPAO","short_pith_number":"pith:NUGSQCLE","canonical_record":{"source":{"id":"1502.05016","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-02-17T20:04:57Z","cross_cats_sorted":[],"title_canon_sha256":"1b27018098a50afdbd1ff116fc802aa6ad31fd8054e210cb1b321dc637eb46b5","abstract_canon_sha256":"47b2152c090472b641a907631f1729e37f3882b64f5d1892b0abdc1b20d08fda"},"schema_version":"1.0"},"canonical_sha256":"6d0d2809648c4dd965a1c09305140f038ce3889663e3aee3b9c39e00c6c26a27","source":{"kind":"arxiv","id":"1502.05016","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.05016","created_at":"2026-05-18T00:29:33Z"},{"alias_kind":"arxiv_version","alias_value":"1502.05016v2","created_at":"2026-05-18T00:29:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.05016","created_at":"2026-05-18T00:29:33Z"},{"alias_kind":"pith_short_12","alias_value":"NUGSQCLERRG5","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"NUGSQCLERRG5SZNB","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"NUGSQCLE","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:NUGSQCLERRG5SZNBYCJQKFAPAO","target":"record","payload":{"canonical_record":{"source":{"id":"1502.05016","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-02-17T20:04:57Z","cross_cats_sorted":[],"title_canon_sha256":"1b27018098a50afdbd1ff116fc802aa6ad31fd8054e210cb1b321dc637eb46b5","abstract_canon_sha256":"47b2152c090472b641a907631f1729e37f3882b64f5d1892b0abdc1b20d08fda"},"schema_version":"1.0"},"canonical_sha256":"6d0d2809648c4dd965a1c09305140f038ce3889663e3aee3b9c39e00c6c26a27","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:33.883588Z","signature_b64":"WJOG6MSV5rPGMx5XspaDhN0iMUon17mICvDdj6O22rnrwOXu9pfxiCRGVT8suMIDmfSGCF7N2nTzZaphkyfxAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d0d2809648c4dd965a1c09305140f038ce3889663e3aee3b9c39e00c6c26a27","last_reissued_at":"2026-05-18T00:29:33.882931Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:33.882931Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.05016","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":"2026-05-18T00:29:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rzB1dx9vzT0XBY6/kG1yiLZa9kEQpH7TBlhhoIrBpNiDeaZmBTIkUw7kTXIyjWfGuVmEOicZgHhWXxd9zg/wCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T09:25:48.877081Z"},"content_sha256":"7345410e19857be895e28fe451bd778846f1d0857cc2799102394807a4eb2b4a","schema_version":"1.0","event_id":"sha256:7345410e19857be895e28fe451bd778846f1d0857cc2799102394807a4eb2b4a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:NUGSQCLERRG5SZNBYCJQKFAPAO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"k-Step Nilpotent Lie Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Elisabeth Remm, Michel Goze","submitted_at":"2015-02-17T20:04:57Z","abstract_excerpt":"The classification of complex of real finite dimensional Lie algebras which are not semi simple is still in its early stages. For example the nilpotent Lie algebras are classified only up to the dimension 7. Moreover, to recognize a given Lie algebra in a classification list is not so easy. In this work we propose a different approach to this problem. We determine families for some fixed invariants, the classification follows by a deformation process or contraction process. We focus on the case of 2 and 3-step nilpotent Lie algebras. We describe in both cases a deformation cohomology of this t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05016","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":"2026-05-18T00:29:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l0Zi73Wm//QiFHepNgVCRRuWMpJnWhvXD0LkInNGRJP5MfO5fsjpCUVmhBIOQzf8/TAPYKYPwte7JghF4GkNAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T09:25:48.877663Z"},"content_sha256":"49d152285b9940dfa7ec1a33a8b9fe6be40a66c34177712e7fa3dda942d45806","schema_version":"1.0","event_id":"sha256:49d152285b9940dfa7ec1a33a8b9fe6be40a66c34177712e7fa3dda942d45806"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NUGSQCLERRG5SZNBYCJQKFAPAO/bundle.json","state_url":"https://pith.science/pith/NUGSQCLERRG5SZNBYCJQKFAPAO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NUGSQCLERRG5SZNBYCJQKFAPAO/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":"2026-05-25T09:25:48Z","links":{"resolver":"https://pith.science/pith/NUGSQCLERRG5SZNBYCJQKFAPAO","bundle":"https://pith.science/pith/NUGSQCLERRG5SZNBYCJQKFAPAO/bundle.json","state":"https://pith.science/pith/NUGSQCLERRG5SZNBYCJQKFAPAO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NUGSQCLERRG5SZNBYCJQKFAPAO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:NUGSQCLERRG5SZNBYCJQKFAPAO","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":"47b2152c090472b641a907631f1729e37f3882b64f5d1892b0abdc1b20d08fda","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-02-17T20:04:57Z","title_canon_sha256":"1b27018098a50afdbd1ff116fc802aa6ad31fd8054e210cb1b321dc637eb46b5"},"schema_version":"1.0","source":{"id":"1502.05016","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.05016","created_at":"2026-05-18T00:29:33Z"},{"alias_kind":"arxiv_version","alias_value":"1502.05016v2","created_at":"2026-05-18T00:29:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.05016","created_at":"2026-05-18T00:29:33Z"},{"alias_kind":"pith_short_12","alias_value":"NUGSQCLERRG5","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"NUGSQCLERRG5SZNB","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"NUGSQCLE","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:49d152285b9940dfa7ec1a33a8b9fe6be40a66c34177712e7fa3dda942d45806","target":"graph","created_at":"2026-05-18T00:29:33Z","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 classification of complex of real finite dimensional Lie algebras which are not semi simple is still in its early stages. For example the nilpotent Lie algebras are classified only up to the dimension 7. Moreover, to recognize a given Lie algebra in a classification list is not so easy. In this work we propose a different approach to this problem. We determine families for some fixed invariants, the classification follows by a deformation process or contraction process. We focus on the case of 2 and 3-step nilpotent Lie algebras. We describe in both cases a deformation cohomology of this t","authors_text":"Elisabeth Remm, Michel Goze","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-02-17T20:04:57Z","title":"k-Step Nilpotent Lie Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05016","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":"sha256:7345410e19857be895e28fe451bd778846f1d0857cc2799102394807a4eb2b4a","target":"record","created_at":"2026-05-18T00:29:33Z","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":"47b2152c090472b641a907631f1729e37f3882b64f5d1892b0abdc1b20d08fda","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-02-17T20:04:57Z","title_canon_sha256":"1b27018098a50afdbd1ff116fc802aa6ad31fd8054e210cb1b321dc637eb46b5"},"schema_version":"1.0","source":{"id":"1502.05016","kind":"arxiv","version":2}},"canonical_sha256":"6d0d2809648c4dd965a1c09305140f038ce3889663e3aee3b9c39e00c6c26a27","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d0d2809648c4dd965a1c09305140f038ce3889663e3aee3b9c39e00c6c26a27","first_computed_at":"2026-05-18T00:29:33.882931Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:33.882931Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WJOG6MSV5rPGMx5XspaDhN0iMUon17mICvDdj6O22rnrwOXu9pfxiCRGVT8suMIDmfSGCF7N2nTzZaphkyfxAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:33.883588Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.05016","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7345410e19857be895e28fe451bd778846f1d0857cc2799102394807a4eb2b4a","sha256:49d152285b9940dfa7ec1a33a8b9fe6be40a66c34177712e7fa3dda942d45806"],"state_sha256":"8b0ec2a5e3c5a26cf880276dc328ae666de2db368e8f2d8245a0cd5f4e643cf4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NXOMDK6CSSHdR9wwyHsKIR8KcRnRU9a4C+Ph02a39qSWNS+zaoSbi70yCi8cgUgc73S6ZXf6wqOnzPiCIyypBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T09:25:48.881000Z","bundle_sha256":"c34247b1ce869785119564bbda4276aecba06b8f0db62177c29f3a8a5881312e"}}