Repulsive periodic-point equidistribution conjecture for non-Archimedean rational maps

Fix a rational map $R$ over $K$ of degree $d\geq 2$. A fixed point $x$ is called repulsive if either $x\in \operatorname{\mathcal{C}}_R\cap \mathbb{H}_K$, or $x\in \mathbb{P}^1_K$ and the multiplier of $R$ at $x$ has norm greater than $1$. For $n\in\mathbb{N}^*$, let $\operatorname{RFix}(R^n)$ be the set of repulsive fixed points of $R^n$, and let $\rho_R$ denote the canonical measure of $R$. Repulsive periodic-point equidistribution conjecture. One has

$$\frac{1}{d^n}\sum_{x\in\operatorname{RFix}(R^n)}\deg_{R^n}(x)\,\delta_x\longrightarrow\rho_R\quad\text{as }n\to+\infty.$$

For arbitrary $K$ with positive Lyapunov exponent, this extends the known equidistribution results for repulsive periodic points; the conjecture is proved in the paper when $R$ is non-wild and $\chi(R)>0$, while the general non-moderate case remains delicate.