Theorem 7.7 bound conjecture for projective hypersurface singularities

Let $Z\subseteq\mathbb{P}^n$ be a hypersurface of degree $d$ with only isolated singular points. Theorem 7.7 gives a bound on the number of these singularities, while Theorem 3.1 gives Varchenko's bound. Bound-comparison conjecture. The bound given in Theorem 7.7 implies the bound given by Varchenko in Theorem 3.1. The preceding discussion says that the relevant arithmetic assertion is left as a conjecture; the source does not establish this implication in general.