The resultant conjecture for self maps of the projective line over function fields

Let $K$ be a function field over a field $k$, and let $\varphi$ be a self map of degree $d$ of $\mathbb{P}^1_K$. Let $R(\varphi)$ be the minimal resultant and let $\mathfrak{f}_{cr}(\varphi)$ be the critical conductor. Let $p$ be the characteristic of $k$, and let $e$ be the inseparability degree of the canonical map induced by $\varphi$ from $\operatorname{Spec}(K)$ to the moduli space $\mathcal{M}_d$. Resultant conjecture for a function field. There exist a constant $C(K)$ and an integer $s(d)$ such that

$$\operatorname{deg}(R(\varphi))\leqslant p^e s(d)(C(K)+\operatorname{deg}(\mathfrak{f}_{cr}(\varphi)) ).$$

The conjecture concerns boundedness of the minimal resultant in terms of the critical conductor, motivated by analogous boundedness results for elliptic curves and their Lattès maps. The source gives no resolution status.