Demailly's conjecture on Waldschmidt constants of point ideals

Suppose that $k$ is an algebraically closed field of characteristic $0$, and let $I$ be the defining ideal of a set of points $X\subseteq \mathbb{P}^n_k$. For an ideal $J$, let $\alpha(J)$ denote the least degree of a nonzero homogeneous element of $J$, and let $m\in\mathbb{N}$. Demailly's conjecture. For every integer $h>1$, one has

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

This generalizes Chudnovsky's lower bound and concerns asymptotic degree growth in symbolic powers of point ideals; the supplied text gives no resolution status.