Demailly's conjecture on initial degrees of symbolic powers

Let $\mathbb{K}$ be an algebraically closed field of characteristic $0$. Let $X\subseteq \mathbb{P}^N_{\mathbb{K}}$ be a set of distinct points, and let $\mathfrak{a}$ be the defining homogeneous ideal of $X$. For a homogeneous ideal $J$, write $\alpha(J)$ for the least degree of a nonzero homogeneous element of $J$, and write $\mathfrak{a}^{(s)}$ for its $s$th symbolic power. Let $r$ be any positive integer.

Demailly's conjecture. For every integer $s\geqslant 1$,

$$\frac{\alpha\left(\mathfrak{a}^{(s)}\right)}{s}\geqslant \frac{\alpha\left(\mathfrak{a}^{(r)}\right)+N-1}{r+N-1}.$$

This generalizes Chudnovsky's bound by allowing the right-hand side to use the initial degree of an arbitrary symbolic power. The supplied text attributes the generalization to Demailly and gives no evidence of resolution.