{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:LDBBM43T536ZJUZRLMGS2UAV5Q","short_pith_number":"pith:LDBBM43T","schema_version":"1.0","canonical_sha256":"58c2167373eefd94d3315b0d2d5015ec292222cef9c7e36b13ce9f3859f47a4d","source":{"kind":"arxiv","id":"1012.4106","version":2},"attestation_state":"computed","paper":{"title":"Equations in simple Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.RA"],"primary_cat":"math.AG","authors_text":"Boris Kunyavskii, Eugene Plotkin, Nikolai Gordeev, Tatiana Bandman","submitted_at":"2010-12-18T17:31:06Z","abstract_excerpt":"Given an element $P(X_1,...,X_d)$ of the finitely generated free Lie algebra, for any Lie algebra $g$ we can consider the induced polynomial map $P: g^d\\to g$. Assuming that $K$ is an arbitrary field of characteristic $\\ne 2$, we prove that if $P$ is not an identity in $sl(2,K)$, then this map is dominant for any Chevalley algebra $g$. This result can be viewed as a weak infinitesimal counterpart of Borel's theorem on the dominancy of the word map on connected semisimple algebraic groups.\n  We prove that for the Engel monomials $[[[X,Y],Y],...,Y]$ and, more generally, for their linear combinat"},"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":"1012.4106","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-12-18T17:31:06Z","cross_cats_sorted":["math.GR","math.RA"],"title_canon_sha256":"24094fba77428aa4e007f4f7846411161345e1ffefe0df683d4102ab85318bb9","abstract_canon_sha256":"b91f146edf082fcf6218ee91ef44750082884d8d7ceab67105b0aa71276b1318"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:27:47.338237Z","signature_b64":"JlDGpMQBOWvoGTzbm+0WyRwXCfV6LG0oViBC181p3qwyUNDpZb4NxczRqvtdp3LiRmYXfm8igAzeBPfnq+BSAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58c2167373eefd94d3315b0d2d5015ec292222cef9c7e36b13ce9f3859f47a4d","last_reissued_at":"2026-05-18T04:27:47.337634Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:27:47.337634Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Equations in simple Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.RA"],"primary_cat":"math.AG","authors_text":"Boris Kunyavskii, Eugene Plotkin, Nikolai Gordeev, Tatiana Bandman","submitted_at":"2010-12-18T17:31:06Z","abstract_excerpt":"Given an element $P(X_1,...,X_d)$ of the finitely generated free Lie algebra, for any Lie algebra $g$ we can consider the induced polynomial map $P: g^d\\to g$. Assuming that $K$ is an arbitrary field of characteristic $\\ne 2$, we prove that if $P$ is not an identity in $sl(2,K)$, then this map is dominant for any Chevalley algebra $g$. This result can be viewed as a weak infinitesimal counterpart of Borel's theorem on the dominancy of the word map on connected semisimple algebraic groups.\n  We prove that for the Engel monomials $[[[X,Y],Y],...,Y]$ and, more generally, for their linear combinat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.4106","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1012.4106","created_at":"2026-05-18T04:27:47.337727+00:00"},{"alias_kind":"arxiv_version","alias_value":"1012.4106v2","created_at":"2026-05-18T04:27:47.337727+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.4106","created_at":"2026-05-18T04:27:47.337727+00:00"},{"alias_kind":"pith_short_12","alias_value":"LDBBM43T536Z","created_at":"2026-05-18T12:26:10.704358+00:00"},{"alias_kind":"pith_short_16","alias_value":"LDBBM43T536ZJUZR","created_at":"2026-05-18T12:26:10.704358+00:00"},{"alias_kind":"pith_short_8","alias_value":"LDBBM43T","created_at":"2026-05-18T12:26:10.704358+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/LDBBM43T536ZJUZRLMGS2UAV5Q","json":"https://pith.science/pith/LDBBM43T536ZJUZRLMGS2UAV5Q.json","graph_json":"https://pith.science/api/pith-number/LDBBM43T536ZJUZRLMGS2UAV5Q/graph.json","events_json":"https://pith.science/api/pith-number/LDBBM43T536ZJUZRLMGS2UAV5Q/events.json","paper":"https://pith.science/paper/LDBBM43T"},"agent_actions":{"view_html":"https://pith.science/pith/LDBBM43T536ZJUZRLMGS2UAV5Q","download_json":"https://pith.science/pith/LDBBM43T536ZJUZRLMGS2UAV5Q.json","view_paper":"https://pith.science/paper/LDBBM43T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1012.4106&json=true","fetch_graph":"https://pith.science/api/pith-number/LDBBM43T536ZJUZRLMGS2UAV5Q/graph.json","fetch_events":"https://pith.science/api/pith-number/LDBBM43T536ZJUZRLMGS2UAV5Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LDBBM43T536ZJUZRLMGS2UAV5Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LDBBM43T536ZJUZRLMGS2UAV5Q/action/storage_attestation","attest_author":"https://pith.science/pith/LDBBM43T536ZJUZRLMGS2UAV5Q/action/author_attestation","sign_citation":"https://pith.science/pith/LDBBM43T536ZJUZRLMGS2UAV5Q/action/citation_signature","submit_replication":"https://pith.science/pith/LDBBM43T536ZJUZRLMGS2UAV5Q/action/replication_record"}},"created_at":"2026-05-18T04:27:47.337727+00:00","updated_at":"2026-05-18T04:27:47.337727+00:00"}