Affine hypersurface dimension growth with the corrected degree exponent: the surface bound d^18 of Proposition 4.3.4 starts the hyperplane-slicing induction, which costs d^3 for each further variable, and clearing denominators passes from integer to rational equations.

theorem CCDN.AffineHypersurfaceGrowth.rational {n e : ℕ} (h : AffineHypersurfaceGrowth n e) : RationalAffineHypersurfaceGrowth n e

Clearing denominators transfers affine dimension growth from integer equations to rational equations with the same constant.

theorem CCDN.affineHypersurfaceGrowth (n : ℕ) : AffineHypersurfaceGrowth n (18 + 3 * n)

Affine dimension growth with degree exponent 18 + 3 * n for integer polynomials in n + 3 variables of degree at least five with absolutely irreducible top-degree form.