{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:IUXS47ZCIKKEXV52NTJZQZEZFC","short_pith_number":"pith:IUXS47ZC","schema_version":"1.0","canonical_sha256":"452f2e7f2242944bd7ba6cd398649928a75fe28969e1662cf40e7d15197bdac9","source":{"kind":"arxiv","id":"1604.05281","version":1},"attestation_state":"computed","paper":{"title":"Higher Jacobi identities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.GR","authors_text":"Ilya Alekseev, Sergei O. Ivanov","submitted_at":"2016-04-18T19:15:17Z","abstract_excerpt":"By definition the identities $[x_1,x_2]+[x_2,x_1]=0$ and $[x_1,x_2,x_3]+[x_2,x_3,x_1]+[x_3,x_1,x_2]=0$ hold in any Lie algebra. It is easy to check that the identity $[x_1,x_2,x_3,x_4]+[x_2,x_1,x_4,x_3]+[x_3,x_4,x_1,x_2]+[x_4,x_3,x_2,x_1] = 0$ holds in any Lie algebra as well. We investigate sets of permutations that give identities of this kind. In particular, we construct a family of such subsets $T_{k,l,n}$ of the symmetric group $S_n,$ and hence, a family of identities that hold in any Lie algebra."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1604.05281","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-04-18T19:15:17Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"fc019b6e6c8d5a25d75913e8336ab12cfe6d5c238691af067ac4e73daf5d6f1b","abstract_canon_sha256":"cadf88eca46aa60ec0bcbe405ecabd4c7bb7adb5fede364cf90beec75d581054"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:55.049962Z","signature_b64":"TCMcy3wVZAZjPUXUR2N9tlyEYMHsf/kNAkh6U465i32wuQmx7i2Df9Qn0Yb0sUJs+QpOGsoBjahvaEt4C4L3AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"452f2e7f2242944bd7ba6cd398649928a75fe28969e1662cf40e7d15197bdac9","last_reissued_at":"2026-05-18T01:16:55.049260Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:55.049260Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Higher Jacobi identities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.GR","authors_text":"Ilya Alekseev, Sergei O. Ivanov","submitted_at":"2016-04-18T19:15:17Z","abstract_excerpt":"By definition the identities $[x_1,x_2]+[x_2,x_1]=0$ and $[x_1,x_2,x_3]+[x_2,x_3,x_1]+[x_3,x_1,x_2]=0$ hold in any Lie algebra. It is easy to check that the identity $[x_1,x_2,x_3,x_4]+[x_2,x_1,x_4,x_3]+[x_3,x_4,x_1,x_2]+[x_4,x_3,x_2,x_1] = 0$ holds in any Lie algebra as well. We investigate sets of permutations that give identities of this kind. In particular, we construct a family of such subsets $T_{k,l,n}$ of the symmetric group $S_n,$ and hence, a family of identities that hold in any Lie algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.05281","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1604.05281","created_at":"2026-05-18T01:16:55.049386+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.05281v1","created_at":"2026-05-18T01:16:55.049386+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.05281","created_at":"2026-05-18T01:16:55.049386+00:00"},{"alias_kind":"pith_short_12","alias_value":"IUXS47ZCIKKE","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_16","alias_value":"IUXS47ZCIKKEXV52","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_8","alias_value":"IUXS47ZC","created_at":"2026-05-18T12:30:22.444734+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IUXS47ZCIKKEXV52NTJZQZEZFC","json":"https://pith.science/pith/IUXS47ZCIKKEXV52NTJZQZEZFC.json","graph_json":"https://pith.science/api/pith-number/IUXS47ZCIKKEXV52NTJZQZEZFC/graph.json","events_json":"https://pith.science/api/pith-number/IUXS47ZCIKKEXV52NTJZQZEZFC/events.json","paper":"https://pith.science/paper/IUXS47ZC"},"agent_actions":{"view_html":"https://pith.science/pith/IUXS47ZCIKKEXV52NTJZQZEZFC","download_json":"https://pith.science/pith/IUXS47ZCIKKEXV52NTJZQZEZFC.json","view_paper":"https://pith.science/paper/IUXS47ZC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.05281&json=true","fetch_graph":"https://pith.science/api/pith-number/IUXS47ZCIKKEXV52NTJZQZEZFC/graph.json","fetch_events":"https://pith.science/api/pith-number/IUXS47ZCIKKEXV52NTJZQZEZFC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IUXS47ZCIKKEXV52NTJZQZEZFC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IUXS47ZCIKKEXV52NTJZQZEZFC/action/storage_attestation","attest_author":"https://pith.science/pith/IUXS47ZCIKKEXV52NTJZQZEZFC/action/author_attestation","sign_citation":"https://pith.science/pith/IUXS47ZCIKKEXV52NTJZQZEZFC/action/citation_signature","submit_replication":"https://pith.science/pith/IUXS47ZCIKKEXV52NTJZQZEZFC/action/replication_record"}},"created_at":"2026-05-18T01:16:55.049386+00:00","updated_at":"2026-05-18T01:16:55.049386+00:00"}