Semi-stable presentations are minimal presentations

Let $\varphi$ be a self map of the projective line and let $\Phi$ be a semi-stable presentation of $\varphi$. A presentation is called minimal when it is minimal at every place. Minimality conjecture. Then $\Phi$ is a minimal presentation of $\varphi$. Semi-stable presentations realize the conductor as their singular reduction locus, a property that every minimal presentation has; the conjecture asks whether the converse implication holds. The source does not indicate whether this is resolved.