Harbourne–Huneke refined Chudnovsky question

Let $I\subseteq\Bbbk[\mathbb P^n]$ be the radical ideal of a finite set of points, and let $\alpha(J)$ denote the least degree of a nonzero homogeneous element of $J$. Fix a positive integer $m$.

Refined Chudnovsky question. For every $r>0$,

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

This asks for a uniform lower bound on all symbolic-power slopes based on one fixed symbolic power; the source presents it as a question and gives no resolution status.