An infinite family of counterexamples to the Jacobian Conjecture in dimension three: every generic fiber degree n≥3 occurs

The Jacobian Conjecture asserts that a polynomial map F: ℂ^n → ℂ^n whose Jacobian determinant is a nonzero constant has a polynomial inverse. On 19 July 2026, L. Alpöge announced an explicit counterexample in dimension three. Building on that example, this preprint gives a uniform one-variable construction which, for every integer n ≥ 3, produces an explicit polynomial map Fₙ: ℂ³ → ℂ³ with det JFₙ ≡ 1 and generic fiber degree exactly n. Thus, in fixed dimension three, non-injective polynomial maps with constant nonzero Jacobian occur in every generic fiber degree n ≥ 3. The degree-four member is neither equivalent to Alpöge’s degree-three map under polynomial coordinate changes nor an iterate of that map.