PomeExample 17.12.13.1A17E2EECB2D Given $\varphi \in \mathrm{PSH}(X,\theta )$, there is a canonically associated test curve $\Gamma ^{\varphi }\in \mathrm{TC}^{\infty }(X,\theta ;V_{\theta })$: Set $\Gamma ^{\varphi }_{\max }=0$ and
\[ \Gamma ^{\varphi }_{\tau }= \begin{cases} V_{\theta },& \textup{if }\tau \leq -1;\\ P_{\theta }\left[ (1+\tau )\varphi -\tau V_{\theta } \right],& \textup{if }-1<\tau <0. \end{cases} \]
Note that $\Gamma ^{\varphi }$ is indeed a test curve, as follows from proposition 16.4.2. Indeed, the concavity and monotonicity in $\tau $ follow from proposition 16.4.2, and $\Gamma ^\varphi _{-\infty }=V_\theta $ has positive mass.
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