Nadirashvili's universal nodal measure lower-bound conjecture

Let $u$ be a harmonic function in $B(0,1)\subset\mathbb{R}^n$ with $u(0)=0$, and let $Z(u)$ denote its nodal set. Nadirashvili's lower-bound conjecture. There exists a universal constant $\delta>0$ such that

$$\mathcal{H}^{n-1}(Z(u)\cap B(0,1))\geq\delta.$$

This weaker-form conjecture supplies a universal lower bound for the nodal measure of a harmonic function vanishing at the center and is related in the source to a generalized Harnack inequality. The source does not state whether it has been resolved.