Linear nodal-volume lower bound for harmonic functions with stable growth

Let $B\subset\mathbb{R}^n$ be a unit ball, with $n\geq 3$, and let $u$ be harmonic in $4B$, vanish at the center of $B$, have stable growth in $B$, and satisfy $\mathcal{N}_u(B)=N\gg1$. Cover $2B$ by a lattice of cubes $Q_i$ of side length $1/N$. The stable-growth lattice conjecture. The number of cubes $Q_i$ in $2B$ that contain a zero of $u$ is at least $cN^n$ for some $c>0$ depending only on $n$. This is a proposed stronger, linear-in-growth description of the distribution of the nodal set; the supplied text gives no resolution, so its status remains open.