The coefficient-uniform affine curve count of CCDN Theorem 3. A bounded integral projection reduces a curve in 𝔸ⁿ to an irreducible plane equation of the same degree, whose points the plane bound PlaneCurveBound counts; exceptional fibres contribute at most d(d − 1) points and the enlarged box costs a constant depending only on n.

theorem CCDN.affine_curve_count : AffineCurveBound

The affine curve counting bound AffineCurveBound of CCDN Theorem 3: the plane bound, after a degree-preserving bounded projection to the plane.