{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:L4S4PSQLAEVGMHHXZ4IVSJV7UT","short_pith_number":"pith:L4S4PSQL","schema_version":"1.0","canonical_sha256":"5f25c7ca0b012a661cf7cf115926bfa4de4d9c5d9cde494191fd149296a199ec","source":{"kind":"arxiv","id":"1311.0232","version":1},"attestation_state":"computed","paper":{"title":"Lie Subalgebras of vector fields and the Jacobian Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Andriy Regeta","submitted_at":"2013-11-01T17:34:07Z","abstract_excerpt":"We study Lie subalgebras $L$ of the vector fields $\\mathrm{Vec}^{c}({\\mathbb A}^{2})$ of affine 2-space ${\\mathbb A}^{2}$ of constant divergence, and we classify those $L$ which are isomorphic to the Lie algebra $\\mathfrak{aff}_{2}$ of the group $\\mathrm{Aff}_{2}(K)$ of affine transformations of ${\\mathbb A}^{2}$. We then show that the following three statements are equivalent: (i) The Jacobian Conjecture holds in dimension 2; (ii) All Lie subalgebras $L \\subset \\mathrm{Vec}^{c}({\\mathbb A}^{2})$ isomorphic to $\\mathfrak{aff}_{2}$ are conjugate under $\\mathrm{Aut}({\\mathbb A}^{2})$; (iii) All "},"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":"1311.0232","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-11-01T17:34:07Z","cross_cats_sorted":[],"title_canon_sha256":"e90cc84243bade3a7a736386242446f464e10a4a73f997253812071ef958235c","abstract_canon_sha256":"de1f630547bdbc8ba9a40943e23c882408d9d2a786f253e43d661c38d8f4e569"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:08:15.263651Z","signature_b64":"kxZ8MgdK9J6oi0U1ECF5Qqk7I3SAnocaCwh1pXzcW/FtgMrbwoCvHnVqHA03rNT9YwSgA0x0RZKTAuW4wBc1AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f25c7ca0b012a661cf7cf115926bfa4de4d9c5d9cde494191fd149296a199ec","last_reissued_at":"2026-05-18T03:08:15.262987Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:08:15.262987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lie Subalgebras of vector fields and the Jacobian Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Andriy Regeta","submitted_at":"2013-11-01T17:34:07Z","abstract_excerpt":"We study Lie subalgebras $L$ of the vector fields $\\mathrm{Vec}^{c}({\\mathbb A}^{2})$ of affine 2-space ${\\mathbb A}^{2}$ of constant divergence, and we classify those $L$ which are isomorphic to the Lie algebra $\\mathfrak{aff}_{2}$ of the group $\\mathrm{Aff}_{2}(K)$ of affine transformations of ${\\mathbb A}^{2}$. We then show that the following three statements are equivalent: (i) The Jacobian Conjecture holds in dimension 2; (ii) All Lie subalgebras $L \\subset \\mathrm{Vec}^{c}({\\mathbb A}^{2})$ isomorphic to $\\mathfrak{aff}_{2}$ are conjugate under $\\mathrm{Aut}({\\mathbb A}^{2})$; (iii) All "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0232","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":"1311.0232","created_at":"2026-05-18T03:08:15.263098+00:00"},{"alias_kind":"arxiv_version","alias_value":"1311.0232v1","created_at":"2026-05-18T03:08:15.263098+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.0232","created_at":"2026-05-18T03:08:15.263098+00:00"},{"alias_kind":"pith_short_12","alias_value":"L4S4PSQLAEVG","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_16","alias_value":"L4S4PSQLAEVGMHHX","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_8","alias_value":"L4S4PSQL","created_at":"2026-05-18T12:27:51.066281+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/L4S4PSQLAEVGMHHXZ4IVSJV7UT","json":"https://pith.science/pith/L4S4PSQLAEVGMHHXZ4IVSJV7UT.json","graph_json":"https://pith.science/api/pith-number/L4S4PSQLAEVGMHHXZ4IVSJV7UT/graph.json","events_json":"https://pith.science/api/pith-number/L4S4PSQLAEVGMHHXZ4IVSJV7UT/events.json","paper":"https://pith.science/paper/L4S4PSQL"},"agent_actions":{"view_html":"https://pith.science/pith/L4S4PSQLAEVGMHHXZ4IVSJV7UT","download_json":"https://pith.science/pith/L4S4PSQLAEVGMHHXZ4IVSJV7UT.json","view_paper":"https://pith.science/paper/L4S4PSQL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1311.0232&json=true","fetch_graph":"https://pith.science/api/pith-number/L4S4PSQLAEVGMHHXZ4IVSJV7UT/graph.json","fetch_events":"https://pith.science/api/pith-number/L4S4PSQLAEVGMHHXZ4IVSJV7UT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/L4S4PSQLAEVGMHHXZ4IVSJV7UT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/L4S4PSQLAEVGMHHXZ4IVSJV7UT/action/storage_attestation","attest_author":"https://pith.science/pith/L4S4PSQLAEVGMHHXZ4IVSJV7UT/action/author_attestation","sign_citation":"https://pith.science/pith/L4S4PSQLAEVGMHHXZ4IVSJV7UT/action/citation_signature","submit_replication":"https://pith.science/pith/L4S4PSQLAEVGMHHXZ4IVSJV7UT/action/replication_record"}},"created_at":"2026-05-18T03:08:15.263098+00:00","updated_at":"2026-05-18T03:08:15.263098+00:00"}