[4] Let $X_{K}$ be a smooth projective K-scheme arising from the base change of an algebraic degeneration family. Let $L$ be an ample line bundle on $X_{K}$, and $d\mu$ be a Radon probability measure supported on the dual intersection complex of some snc model of $X_{K}$. Then there is a unique continuous semipositive metric $\left\lVert\cdot\right\rVert$ on $L$, such that