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The result does not hold for larger n.\n  The proof of the case det Hf in K* is based on the following result, whic"},"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":"1203.6605","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-03-29T17:41:06Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"ca5d0fa64f4150f160183533a30d46315959ddd9a5e451e38ca7201e287730f6","abstract_canon_sha256":"d50eee25adc710ee35eacec6d38cc7f631d3c133f727dd8c2401d28d2d85c4f1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:02.812103Z","signature_b64":"6jr64Xg47xHuc61VmyOqQsrVoyeQsac+zsyEshNoKf3tSAVWH7RPyMC+pAcBX06yQSzpuaMLNsz80QvcyKsYAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1401e9a75ecc4c4dde7395fb02e727b9e292bdfcaf69962580aeb565d6f9fdc6","last_reissued_at":"2026-05-18T02:29:02.811648Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:02.811648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Polynomials with constant Hessian determinants in dimension three","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Michiel de Bondt","submitted_at":"2012-03-29T17:41:06Z","abstract_excerpt":"In this paper, we show that the Jacobian conjecture holds for gradient maps in dimension n <= 3 over a field K of characteristic zero. 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