is $$\sum_{i = 1}^n m_i x_i$$ where $m_i$ is the sum of the outgoing slopes of $F$ at $x_i$. The principal divisors on $\Gamma$ form a subgroup, which we call $\operatorname{Prin}_\Lambda(\Gamma)$.

If $\tau \colon {X^{\rm an}}\to \Gamma$ is the deformation retraction of ${X^{\rm an}}$ onto its skeleton, then $\tau$ maps $X(K)$ onto $\Gamma(\Lambda)$. We can therefore extend this map to a surjective map $\tau_* \colon \operatorname{Div}(X) \to \operatorname{Div}_\Lambda(\Gamma)$.

Let $f \in K(X)^*$ be a rational function. Then $\log|f|$ is a function on ${X^{\rm an}}$. If $F$ is the restriction of $\log|f|$ to $\Gamma$, then it is known that $F$ is a $\Lambda$-rational function. Moreover, $$\tau_*\operatorname{div}(f) = \operatorname{div}(F).$$ This means that $\tau_*$ takes principal divisors to principal divisors.

These two facts about $\log|f|$ are referred to as the “slope formula” or “non-Archimedean Poincaré-Lelong formula” in the literature. The formula was first stated and proved in our terminology by Baker, Payne and Rabinoff [@BPR13], Theorem 5.15. The original result is due to Thuiller [@Thu] who phrased it in terms of potential theory. Thuiller’s formulation closely resembles the classical formula for complex manifolds.

More results about the connection between $\operatorname{Div}(X)$ and $\operatorname{Div}_\Lambda(\Gamma)$ may be found in [@Baker] and [@BR].

An effective divisor $B$ 