{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:LP6UZKUMPC2TYLEXJ7WKS6ZK2T","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":"3880eac0bf36dcfd1ccee0ab82f24e64886d63a8ed4d7c98bbd71b1834d12e6c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-02-20T14:38:31Z","title_canon_sha256":"38a2c87e7fc66a47e2310060a2716c08a199ff277d1cfbe2a3ac1665d44ab8d9"},"schema_version":"1.0","source":{"id":"1402.5012","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.5012","created_at":"2026-05-18T02:58:31Z"},{"alias_kind":"arxiv_version","alias_value":"1402.5012v1","created_at":"2026-05-18T02:58:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.5012","created_at":"2026-05-18T02:58:31Z"},{"alias_kind":"pith_short_12","alias_value":"LP6UZKUMPC2T","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LP6UZKUMPC2TYLEX","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LP6UZKUM","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:cb77d15692fab769c1649bdbbea9a8050cfdf432e468931da704a8c0345e1c8d","target":"graph","created_at":"2026-05-18T02:58:31Z","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 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","authors_text":"Andriy Regeta, Hanspeter Kraft","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-02-20T14:38:31Z","title":"Automorphisms of the Lie algebra of vector fields on affine n-space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.5012","kind":"arxiv","version":1},"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:f0a25c9182630e54ffb700490e05d55ac618843633c3ea55bb312b2ff644ef46","target":"record","created_at":"2026-05-18T02:58:31Z","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":"3880eac0bf36dcfd1ccee0ab82f24e64886d63a8ed4d7c98bbd71b1834d12e6c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-02-20T14:38:31Z","title_canon_sha256":"38a2c87e7fc66a47e2310060a2716c08a199ff277d1cfbe2a3ac1665d44ab8d9"},"schema_version":"1.0","source":{"id":"1402.5012","kind":"arxiv","version":1}},"canonical_sha256":"5bfd4caa8c78b53c2c974feca97b2ad4f7ea398c9188e1acd8ad7924bbe3a6d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5bfd4caa8c78b53c2c974feca97b2ad4f7ea398c9188e1acd8ad7924bbe3a6d2","first_computed_at":"2026-05-18T02:58:31.369724Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:31.369724Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0pt5YK3V187e+vCE9m5wN9Txnh1P7lQDo1smfCMm7v/9/0UNDICiUw2vq7wIChkmFn1yj3uA+6CptCtDy3gBAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:31.370466Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.5012","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f0a25c9182630e54ffb700490e05d55ac618843633c3ea55bb312b2ff644ef46","sha256:cb77d15692fab769c1649bdbbea9a8050cfdf432e468931da704a8c0345e1c8d"],"state_sha256":"2745e832125e311f60aa506e5afde38df106676e3e4335722a9ed2059af35501"}