(Metric deviation) For $x_{1}^{\prime}\gg 1$, then in the region with $|x_{1}-x_{1}^{\prime}|\leq x_{1}^{\prime\frac{n-2}{2(n-1)}}$ and $|x_{2}|\ll x_{1}^{\prime}$, the metric deviation between $dd^{c}\phi_{D_{1}}$ and the local product metric (32) satisfies the local $C^{k,\alpha}$ estimate on $O(\rho)$ neighbourhoods around a given point: