(Metric $C^{\infty}_{loc}$-convergence in the generic region) For any given $0<\delta\ll 1$, then as $t\to 0$,

$$\left\lVert\phi_{CY,J,t}-\phi_{0}\circ\text{Log}_{\mathcal{X}}\right\rVert_{C^{k}(\text{Log}_{\mathcal{X}}^{-1}(W_{\delta}))}\to 0,$$

where the $C^{k}$-norm is defined by passing to the local universal cover of $\text{Log}_{\mathcal{X}}^{-1}(W_{\delta})\subset(\mathbb{C}^{*})^{n}$ with preferred coordinates $\zeta_{i}=\frac{1}{\log|t|}\log z_{i}$ for $i=1,2,\ldots,n$.