Bocci–Cooper–Harbourne generalized symbolic-power containment conjecture

Let $I\subseteq\Bbbk[\mathbb P^n]$ be the radical ideal of a finite set of points in $\mathbb P^n$, and let $\mathfrak m=(x_0,\ldots,x_n)$ be the maximal proper homogeneous ideal. Let $m,t$ be positive integers.

Bocci–Cooper–Harbourne conjecture. For all $m\geq1$,

$$I^{(t(m+n-1)-n+1)}\subseteq\mathfrak m^{(t-1)(n-1)}\bigl(I^{(m)}\bigr)^t.$$

The source introduces this as a further conjecture while discussing special cases of the preceding containment questions; it gives no resolution status.