Magnanini's critical-point conjecture for the landscape function

Let $\Omega$ be simply-connected, let $v$ be its landscape function, and let $N$ be the number of critical points of $v$ in $\Omega$. Define

$$d_{\partial\Omega}(z)=\operatorname{dist}(z,\partial\Omega),$$

and let $m$ be the number of maxima in $\Omega$ of this distance-to-the-boundary function.

Magnanini's conjecture. The number of critical points satisfies

$$N\leq 2m-1.$$

The source recalls this conjecture as an attribution to R. Magnanini; it does not state that the conjecture has been resolved.