do not make use of in this paper.

Skeleta and extended skeleta of curves
--------------------------------------

When $X$ is a curve, there exists a distinguished set $\Gamma \subset {X^{\rm an}}$ called a *skeleton of $X$ (or of ${X^{\rm an}}$)* with the following key properties.

1.  A skeleton is a metric graph.

2.  There is a strong deformation retract $\tau \colon {X^{\rm an}}\to \Gamma$.

3.  The map $\tau_* \colon \operatorname{Div}(X) \to \operatorname{Div}_\Lambda(\Gamma)$ is surjective and takes principal divisors to principal divisors. We define the divisor group of $\Gamma$ in Subsection \[sec:skel-div\].

We start by defining skeletons for open discs and open annuli. More detail is given in [@BPR13 Section 2].

\[def:open-annuli\] Let ${\mathbf}{A}^{1,\operatorname{an}} = (\operatorname{Spec}K[T])^{\operatorname{an}}$. We call the sets $$B(r) \coloneqq \{x \in {\mathbf}{A}^{1,\operatorname{an}} : |T|_x < r\} \text{ and } A(r,s) \coloneqq \{x \in {\mathbf}{A}^{1,\operatorname{an}} : r < \log |T|_x < s\}$$ *open discs* and *open annuli* respectively. They are parameterized by real numbers $r, s$ which we call *logarithmic radii*. For an open annulus, we also allow $r = -\infty$ in which case $A(-\infty,s)$ is a *punctured disc*.

The disc $B(t)$ has a distinguished element $\rho_{B(t)}$ defined by $${\left\lvert \sum a_i T^i \right\rvert}_{\rho_{B(t)}} = \max\limits_i |a_i| t^i.$$ As the disc 