The refined Chudnovsky conjecture for symbolic initial degrees

Let $K$ be an algebraically closed field, let $I$ be the radical ideal of a finite set of points in $\mathbb{P}^{N}$, and let $\alpha(I)$ denote the least degree of a nonzero form in $I$. Refined Chudnovsky conjecture. For every $r>0$,

$$\frac{\alpha(I^{(m)})+N-1}{m+N-1}\leq\frac{\alpha(I^{(r)})}{r}.$$

This refines the Waldschmidt-type lower bounds for symbolic powers; the source labels it as a question and gives no resolution evidence.