Let $\Delta$ be a skeleton associated to a strongly nondegenerate strictly polystable formal scheme $\mathfrak{X}^{\prime}$ over $K^{\circ}$. A continuous function $h:\Delta\rightarrow\mathbb{R}$ is called piecewise affine linear if there exists a $\Gamma$-rational polytopal subdivision $\mathfrak{D}$ of $\Delta$ such that for any canonical polysimplex $\Delta_{S}$ of $\Delta$, any formal open subset $\psi:\mathfrak{U}\rightarrow\mathfrak{X}(\boldsymbol{n},\boldsymbol{a},m)$ of $\mathfrak{X}^{\prime}$ whose distinguished stratum is $S$ and any $\Delta^{\prime}\in\mathfrak{D}$ with $\Delta^{\prime}\subseteq\Delta_{S}$, there exist $\boldsymbol{m}\in\mathbb{Z}^{\boldsymbol{n}+\boldsymbol{1}}$ and $\alpha\in K^{\times}$ such that $h\Big|_{\Delta^{\prime}}=(\boldsymbol{m}\cdot\boldsymbol{x}+v(\alpha))\circ\psi^{\textup{an}}\Big|_{\Delta^{\prime}}$ (see Definition 2.3 for the notation and setting).