Rationally independent edge-length hot-spots conjecture

Let $n\geq 2$. A metric graph $amma$ is said to have pairwise rationally independent edge lengths when no nontrivial rational relation holds among its edge lengths. Let $M$ be the set of global minima and maxima of second eigenfunctions on $amma$.

Rationally independent edge-length conjecture. There exists a graph $\gamma$ whose edge lengths are pairwise rationally independent and for which $|M|=3$; more generally, for every prescribed $n\geq 2$, there exists such a graph with $|M|=n$.

This conjecture asserts that multiple hot spots can occur without symmetry or commensurability of edge lengths. The source gives no resolution status.