Combine the uniform $C^{0}$-estimate Theorem 2.2 and the uniform Skoda estimate Theorem 2.1, we know the CY potential with respect to any fixed choice of Fubini-Study background metric is uniformly bounded for small $t$. Here the implicit choice of $\epsilon$ in $\omega_{FS,t}$ does not matter because of Lemma 4.1. ∎