There is a homeomorphism $\overline{{\mathbb{D}}}_{r}\overset{\sim}{\to}{\mathcal{M}}(A_{r})\simeq C_{\mathrm{hyb}}(r)$, that maps $z\in\overline{{\mathbb{D}}}_{r}\subset{\mathbb{C}}$ to the seminorm on $A_{r}$ defined by

$$|f|=\begin{cases}r^{\operatorname{ord}_{0}(f)}&\ \text{if $z=0$}\\ r^{\frac{\log|f^{\operatorname{hol}}(z)|_{\infty}}{\log|z|_{\infty}}}\ &\text{otherwise},\end{cases}$$

(A.1)

and via which the map $\lambda\colon C_{\mathrm{hyb}}(r)\to[0,1]$ is given by $\lambda(z)=\frac{\log r}{\log|z|_{\infty}}$.