Harbourne–Huneke degree-bound conjecture for symbolic powers

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

Harbourne–Huneke degree-bound conjecture. For every $r>0$,

$$\alpha\bigl(I^{(rn-(n-1))}\bigr)\geq r\alpha(I)+(r-1)(n-1).$$

This is the degree-theoretic counterpart of the preceding maximal-ideal containment conjecture; the source gives no resolution status.