Using the metric deviation estimate, the Riemannian curvature is bounded. Morever if $\ell>2A^{-1/4}$, then we can find a flat model $g_{\text{flat}}$ over a $g_{a}$-ball of radius $\sim\ell/10$, where $\left\lVert g_{\text{flat}}-g_{\mathbb{C}^{3}}\right\rVert_{C^{k,\alpha}_{-1,0}}\leq C.$ Using this bound up to second order derivatives, the Christoffel symbols in the local flat coordinates are $O(A^{-1/4}\ell^{-2})$ and the Riemannian curvature is of order $O(A^{-1/4}\ell^{-3})$. ∎