Connected p.c.f self-similar fractals satisfying the angle separation condition have conformal dimension 1

Let ${\mathcal G}$ be a graph-directed iterated function system (GIFS) satisfying the finite post-critical points property (p.c.f), and assume that the attractors $(M_\ell)_{\ell\in{\mathcal L}}$ are connected. In this paper, we use valuation pairs to construct new metrics on the attractor of ${\mat