Minimally critical regular endomorphisms of A^N

The paper’s Theorem 3 is correctly stated and proved via careful local (place-by-place) inequalities for divisors using the λ/µ formalism and a relative escape-rate Δf, then summed globally to obtain bounds with constants depending only on N and d. The candidate solution captures the right setup (L∘φ model, critical divisor decomposition, relative height idea) and arrives at inequalities of the right qualitative form, but it relies on an unjustified uniform comparison between canonical heights of hyperplanes and single-step coefficient heights that would, in general, depend on the specific map f. This misses the paper’s key technical ingredient that yields uniform-in-(A,b) constants and the sharper A−1 contribution. Hence the model’s proof is not complete/correct as written, while the paper’s proof is.