{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:LP6UZKUMPC2TYLEXJ7WKS6ZK2T","short_pith_number":"pith:LP6UZKUM","schema_version":"1.0","canonical_sha256":"5bfd4caa8c78b53c2c974feca97b2ad4f7ea398c9188e1acd8ad7924bbe3a6d2","source":{"kind":"arxiv","id":"1402.5012","version":1},"attestation_state":"computed","paper":{"title":"Automorphisms of the Lie algebra of vector fields on affine n-space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Andriy Regeta, Hanspeter Kraft","submitted_at":"2014-02-20T14:38:31Z","abstract_excerpt":"We show that every Lie algebra automorphisms of the vector fields $Vec(A^n)$ of affine n-space $A^n$, of the vector fields $Vec^c(A^n)$ with constant divergence, and of the vector fields $Vec^0(A^n)$ with divergence zero is induced by an automorphism of $A^n$. This generalizes results of the second author obtained in dimension 2. The case of $Vec(A^n)$ is due to Vladimir Bavula. As an immediate consequence, we get the following result which due to Viktor Kulikov. If every injective endomorphism of the simple Lie algebra $Vec(A^n)$ is an automorphism, then the Jacobian Conjecture holds in dimen"},"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":"1402.5012","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-02-20T14:38:31Z","cross_cats_sorted":[],"title_canon_sha256":"38a2c87e7fc66a47e2310060a2716c08a199ff277d1cfbe2a3ac1665d44ab8d9","abstract_canon_sha256":"3880eac0bf36dcfd1ccee0ab82f24e64886d63a8ed4d7c98bbd71b1834d12e6c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:31.370466Z","signature_b64":"0pt5YK3V187e+vCE9m5wN9Txnh1P7lQDo1smfCMm7v/9/0UNDICiUw2vq7wIChkmFn1yj3uA+6CptCtDy3gBAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5bfd4caa8c78b53c2c974feca97b2ad4f7ea398c9188e1acd8ad7924bbe3a6d2","last_reissued_at":"2026-05-18T02:58:31.369724Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:31.369724Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Automorphisms of the Lie algebra of vector fields on affine n-space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Andriy Regeta, Hanspeter Kraft","submitted_at":"2014-02-20T14:38:31Z","abstract_excerpt":"We show that every Lie algebra automorphisms of the vector fields $Vec(A^n)$ of affine n-space $A^n$, of the vector fields $Vec^c(A^n)$ with constant divergence, and of the vector fields $Vec^0(A^n)$ with divergence zero is induced by an automorphism of $A^n$. This generalizes results of the second author obtained in dimension 2. The case of $Vec(A^n)$ is due to Vladimir Bavula. As an immediate consequence, we get the following result which due to Viktor Kulikov. If every injective endomorphism of the simple Lie algebra $Vec(A^n)$ is an automorphism, then the Jacobian Conjecture holds in dimen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.5012","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":"1402.5012","created_at":"2026-05-18T02:58:31.369842+00:00"},{"alias_kind":"arxiv_version","alias_value":"1402.5012v1","created_at":"2026-05-18T02:58:31.369842+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.5012","created_at":"2026-05-18T02:58:31.369842+00:00"},{"alias_kind":"pith_short_12","alias_value":"LP6UZKUMPC2T","created_at":"2026-05-18T12:28:38.356838+00:00"},{"alias_kind":"pith_short_16","alias_value":"LP6UZKUMPC2TYLEX","created_at":"2026-05-18T12:28:38.356838+00:00"},{"alias_kind":"pith_short_8","alias_value":"LP6UZKUM","created_at":"2026-05-18T12:28:38.356838+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/LP6UZKUMPC2TYLEXJ7WKS6ZK2T","json":"https://pith.science/pith/LP6UZKUMPC2TYLEXJ7WKS6ZK2T.json","graph_json":"https://pith.science/api/pith-number/LP6UZKUMPC2TYLEXJ7WKS6ZK2T/graph.json","events_json":"https://pith.science/api/pith-number/LP6UZKUMPC2TYLEXJ7WKS6ZK2T/events.json","paper":"https://pith.science/paper/LP6UZKUM"},"agent_actions":{"view_html":"https://pith.science/pith/LP6UZKUMPC2TYLEXJ7WKS6ZK2T","download_json":"https://pith.science/pith/LP6UZKUMPC2TYLEXJ7WKS6ZK2T.json","view_paper":"https://pith.science/paper/LP6UZKUM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1402.5012&json=true","fetch_graph":"https://pith.science/api/pith-number/LP6UZKUMPC2TYLEXJ7WKS6ZK2T/graph.json","fetch_events":"https://pith.science/api/pith-number/LP6UZKUMPC2TYLEXJ7WKS6ZK2T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LP6UZKUMPC2TYLEXJ7WKS6ZK2T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LP6UZKUMPC2TYLEXJ7WKS6ZK2T/action/storage_attestation","attest_author":"https://pith.science/pith/LP6UZKUMPC2TYLEXJ7WKS6ZK2T/action/author_attestation","sign_citation":"https://pith.science/pith/LP6UZKUMPC2TYLEXJ7WKS6ZK2T/action/citation_signature","submit_replication":"https://pith.science/pith/LP6UZKUMPC2TYLEXJ7WKS6ZK2T/action/replication_record"}},"created_at":"2026-05-18T02:58:31.369842+00:00","updated_at":"2026-05-18T02:58:31.369842+00:00"}