Silverman's height comparison conjecture for rational maps

For an individual rational function $f\in\operatorname{Rat}_d(k)$, let $h_{\operatorname{crit},\mathbb{Q}}$ be the critical height on the moduli space $\mathrm{M}_d$, and let $h_{\mathrm{M}_d,D,\mathbb{Q}}$ be the height associated with a divisor $D$. Let $\mathrm{L}_d$ denote the flexible Lattès locus in $\mathrm{M}_d$. Silverman's conjecture. There are constants $A_1,A_2>0$ and $B_1,B_2\in\mathbb{R}$ such that

$$A_1\cdot h_{\mathrm{M}_d,D,\mathbb{Q}}+B_1\le h_{\operatorname{crit},\mathbb{Q}}\le A_2\cdot h_{\mathrm{M}_d,D,\mathbb{Q}}+B_2$$

on $(\mathrm{M}_d\setminus\mathrm{L}_d)(\overline{\mathbb{Q}})$. The conjecture gives a two-sided comparison between the critical height and a moduli-space height away from the flexible Lattès locus; the lower bound was later established by Ingram, and the supplied source evidence states that the conjecture was answered effectively by Gauthier, Okuyama, and Vigny.