A dimension induction with a cubic degree cost per hyperplane slice, using the constructed universal Noether detector.

Integer equations for every parallel level of a good hyperplane whose normal has cubic degree height.

theorem CCDN.affineHypersurfaceGrowth_of_surface {e : ℕ} (h : AffineHypersurfaceGrowth 0 e) (n : ℕ) : AffineHypersurfaceGrowth n (e + 3 * n)

Bounded good hyperplanes lift a surface bound with degree exponent e to every higher dimension; each slice adds three to the exponent.