Generic Newton slope conjecture for dominant affine Weyl elements

Let $G=SL_n(F)$, let $x=\pi^{\mu}w\in\widetilde{W}$, and suppose that $\mu$ is dominant, meaning

$$\langle\alpha_i,\mu\rangle\geq 0$$

for every simple root $\alpha_i$ in $\operatorname{Lie}(G)$, equivalently $\mu_1\geq\cdots\geq\mu_n$. Let $\nu_x$ denote the generic Newton slope sequence associated to $x$, and let $\mu_{\operatorname{dom}}$ denote the dominant representative of $\mu$. Generic Newton slope conjecture. Then

$$\nu_x=-\mu_{\operatorname{dom}}.$$

The conjecture seeks a root-theoretic formula for the generic Newton slope in the Iwahori case, analogous to Mazur's inequality; the source gives no resolution status.