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We bring two ideas concerning the Jacobian Conjecture: First, we conjecture that for all $n$, the degree of the field extension $\\mathbb{C}(F(x_1),\\ldots,F(x_n)) \\subseteq \\mathbb{C}(x_1,\\ldots,x_n)$ is less than or equal to $d^{n-1}$, where $d$ is the minimum of the degrees of the $F(x_i)$'s. If this conjecture is true, then the generalized Jacobian Conjecture is true. Second, we suggest to replace in some known theorems the assumption on the degrees of the"},"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":"1610.01621","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-08-24T19:57:08Z","cross_cats_sorted":[],"title_canon_sha256":"dedff5d6e2b59639e3025ed773fb9ac36dc6c8ba20533a650f4687b12035c6e1","abstract_canon_sha256":"6b8908db2a5f1f3dcedf9a9d8a6c7d8a35fd3e82da7107afaea5442fa66b1e8b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:05.390170Z","signature_b64":"OkM8iWSutVoqd3MvqjI4OLGrGNPFZjhkjmaZpCrEaYxAJUDl47yVMFlkV9AelVfVRA0Eg8AhBK7zXJnP4uP/Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd12407625fc0fcfef24a3a3fbb12892f9f1a8456474d5b96ac2aad8b0f2ee71","last_reissued_at":"2026-05-18T01:03:05.389663Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:05.389663Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ideas about the Jacobian Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Vered Moskowicz","submitted_at":"2016-08-24T19:57:08Z","abstract_excerpt":"Let $F:\\mathbb{C}[x_1,\\ldots,x_n] \\to \\mathbb{C}[x_1,\\ldots,x_n]$ be a $\\mathbb{C}$-algebra endomorphism that has an invertible Jacobian. We bring two ideas concerning the Jacobian Conjecture: First, we conjecture that for all $n$, the degree of the field extension $\\mathbb{C}(F(x_1),\\ldots,F(x_n)) \\subseteq \\mathbb{C}(x_1,\\ldots,x_n)$ is less than or equal to $d^{n-1}$, where $d$ is the minimum of the degrees of the $F(x_i)$'s. If this conjecture is true, then the generalized Jacobian Conjecture is true. 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