Forest conjecture for supports of asymptotic derivative measures

Let $P$ be a polynomial and let $\x03bc_{\x03b1,P}$ be the asymptotic root-counting measure from Theorem~. Forest conjecture. For $0<\x03b1<\deg P$, the support of $\x03bc_{\x03b1,P}$ is an embedded graph in $\x1d53d$ without cycles; equivalently, it is a forest. This is motivated by numerical experiments, including the cubic case, but the source supplies no proof or resolution.