{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:WVM3V6CRP3SFGX3KBLXL4Y7YNV","short_pith_number":"pith:WVM3V6CR","canonical_record":{"source":{"id":"1201.2674","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-01-12T20:55:39Z","cross_cats_sorted":[],"title_canon_sha256":"186fd0eeb9366248df8579814f5ba69a27f1040c51b53e4b098fc51d64cedb96","abstract_canon_sha256":"5057753d26adcb16d30d963429fe66259b4d478863507cad580b45ee25eafdfa"},"schema_version":"1.0"},"canonical_sha256":"b559baf8517ee4535f6a0aeebe63f86d49d82c7bc291c8f24b81774983226459","source":{"kind":"arxiv","id":"1201.2674","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.2674","created_at":"2026-05-18T03:11:09Z"},{"alias_kind":"arxiv_version","alias_value":"1201.2674v3","created_at":"2026-05-18T03:11:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.2674","created_at":"2026-05-18T03:11:09Z"},{"alias_kind":"pith_short_12","alias_value":"WVM3V6CRP3SF","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"WVM3V6CRP3SFGX3K","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"WVM3V6CR","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:WVM3V6CRP3SFGX3KBLXL4Y7YNV","target":"record","payload":{"canonical_record":{"source":{"id":"1201.2674","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-01-12T20:55:39Z","cross_cats_sorted":[],"title_canon_sha256":"186fd0eeb9366248df8579814f5ba69a27f1040c51b53e4b098fc51d64cedb96","abstract_canon_sha256":"5057753d26adcb16d30d963429fe66259b4d478863507cad580b45ee25eafdfa"},"schema_version":"1.0"},"canonical_sha256":"b559baf8517ee4535f6a0aeebe63f86d49d82c7bc291c8f24b81774983226459","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:09.763641Z","signature_b64":"opSDn4w+QLqdSQXJ1eQKNez/wcLnQl9ha3iJ5wGNyTjfAzmgNTwhTxEClimLMcGkxTfMq7ixz67sFzTF06V0DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b559baf8517ee4535f6a0aeebe63f86d49d82c7bc291c8f24b81774983226459","last_reissued_at":"2026-05-18T03:11:09.762889Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:09.762889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.2674","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:11:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s5l0OQ+E4nXvNjS8YFW/2ABfK4u2lHedZ+uiGbBGw+FpsYbGD3Rnped0ENmS4BTAWbBFOwScrjK97UIt5l53Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T13:55:52.012566Z"},"content_sha256":"a52b0062ce1ede74b2f3582887d3801f6e4d278953728d9b845f2cfa4bf7f5bc","schema_version":"1.0","event_id":"sha256:a52b0062ce1ede74b2f3582887d3801f6e4d278953728d9b845f2cfa4bf7f5bc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:WVM3V6CRP3SFGX3KBLXL4Y7YNV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lie algebras with associative structures. Applications to the study of 2-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":"2012-01-12T20:55:39Z","abstract_excerpt":"We investigate Lie algebras whose Lie bracket is also an associative or cubic associative multiplication to characterize the class of nilpotent Lie algebras with a nilindex equal to 2 or 3. In particular we study the class of 2-step nilpotent Lie algebras, their deformations and we compute the cohomology which parametrize the deformations in this class."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.2674","kind":"arxiv","version":3},"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":"2026-05-18T03:11:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bGVTOxZ3fv68DKj47YpgRS7SQdU6ASEWPW9pwm/7NY7GvyUAj3sAOYwswXYoPZ020Cohn2H6+oN+0kwXXzL3AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T13:55:52.013195Z"},"content_sha256":"02943331822f9823c2ac9c37cec27884377d0f11196ea039bbc9e5506c6a0de0","schema_version":"1.0","event_id":"sha256:02943331822f9823c2ac9c37cec27884377d0f11196ea039bbc9e5506c6a0de0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WVM3V6CRP3SFGX3KBLXL4Y7YNV/bundle.json","state_url":"https://pith.science/pith/WVM3V6CRP3SFGX3KBLXL4Y7YNV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WVM3V6CRP3SFGX3KBLXL4Y7YNV/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":"2026-06-01T13:55:52Z","links":{"resolver":"https://pith.science/pith/WVM3V6CRP3SFGX3KBLXL4Y7YNV","bundle":"https://pith.science/pith/WVM3V6CRP3SFGX3KBLXL4Y7YNV/bundle.json","state":"https://pith.science/pith/WVM3V6CRP3SFGX3KBLXL4Y7YNV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WVM3V6CRP3SFGX3KBLXL4Y7YNV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:WVM3V6CRP3SFGX3KBLXL4Y7YNV","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":"5057753d26adcb16d30d963429fe66259b4d478863507cad580b45ee25eafdfa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-01-12T20:55:39Z","title_canon_sha256":"186fd0eeb9366248df8579814f5ba69a27f1040c51b53e4b098fc51d64cedb96"},"schema_version":"1.0","source":{"id":"1201.2674","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.2674","created_at":"2026-05-18T03:11:09Z"},{"alias_kind":"arxiv_version","alias_value":"1201.2674v3","created_at":"2026-05-18T03:11:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.2674","created_at":"2026-05-18T03:11:09Z"},{"alias_kind":"pith_short_12","alias_value":"WVM3V6CRP3SF","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"WVM3V6CRP3SFGX3K","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"WVM3V6CR","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:02943331822f9823c2ac9c37cec27884377d0f11196ea039bbc9e5506c6a0de0","target":"graph","created_at":"2026-05-18T03:11:09Z","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":"We investigate Lie algebras whose Lie bracket is also an associative or cubic associative multiplication to characterize the class of nilpotent Lie algebras with a nilindex equal to 2 or 3. In particular we study the class of 2-step nilpotent Lie algebras, their deformations and we compute the cohomology which parametrize the deformations in this class.","authors_text":"Elisabeth Remm, Michel Goze","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-01-12T20:55:39Z","title":"Lie algebras with associative structures. Applications to the study of 2-step nilpotent Lie algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.2674","kind":"arxiv","version":3},"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:a52b0062ce1ede74b2f3582887d3801f6e4d278953728d9b845f2cfa4bf7f5bc","target":"record","created_at":"2026-05-18T03:11:09Z","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":"5057753d26adcb16d30d963429fe66259b4d478863507cad580b45ee25eafdfa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-01-12T20:55:39Z","title_canon_sha256":"186fd0eeb9366248df8579814f5ba69a27f1040c51b53e4b098fc51d64cedb96"},"schema_version":"1.0","source":{"id":"1201.2674","kind":"arxiv","version":3}},"canonical_sha256":"b559baf8517ee4535f6a0aeebe63f86d49d82c7bc291c8f24b81774983226459","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b559baf8517ee4535f6a0aeebe63f86d49d82c7bc291c8f24b81774983226459","first_computed_at":"2026-05-18T03:11:09.762889Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:09.762889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"opSDn4w+QLqdSQXJ1eQKNez/wcLnQl9ha3iJ5wGNyTjfAzmgNTwhTxEClimLMcGkxTfMq7ixz67sFzTF06V0DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:09.763641Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.2674","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a52b0062ce1ede74b2f3582887d3801f6e4d278953728d9b845f2cfa4bf7f5bc","sha256:02943331822f9823c2ac9c37cec27884377d0f11196ea039bbc9e5506c6a0de0"],"state_sha256":"a2e16708bb11545223f98625d61a7c204d729b4d066d17c60fa5b35c1a98accc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MS64FKrg6wMzQAQBslpCEA+Kt2px7gl+5ymA3SZFp7TFVc1TiB0rfncGqzeC5BpjojFT7V9yH1qG+ddYUmzDBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T13:55:52.016116Z","bundle_sha256":"ce5cff8b8b5c03db0096d98a5e95b1ed5f5469e020d910fbab3fa74c6988a712"}}