Nonproperness sets in a weighted-lift family of Keller maps

We study a family F_p : C³ → C³ of Keller maps associated with one-variable seed polynomials p. We reduce the inverse problem to a polynomial equation of degree deg p + 1 and determine the complete nonproperness set S{F_p}. For quadratic seeds, S{F_p} is an irreducible discriminant surface. For every seed of degree at least three, S_{F_p} has exactly two irreducible components: the discriminant surface and an additional affine plane. We construct two explicit determinant-one subfamilies and show that, for every generic fiber degree n ≥ 4, they are inequivalent under polynomial automorphisms of source and target. The distinction is detected by generic fiber cardinalities along the irreducible components of the nonproperness set. Working manuscript, not peer reviewed. The deposit includes the LaTeX source and two machine-checkable companions: an exact SymPy verification script and a sorry-free Lean 4 formalization of the core algebraic identities (pinned to Lean/mathlib v4.32.1). Builds on the July 2026 three-dimensional counterexample to the Jacobian conjecture and cites the anonymous Ulam AI preprint as prior art for the single-map case.