Suppose $(X,g,J,L,A)$ is in ${\mathcal{K}}(n,c,V)$ and $(U,D,u_{*})$ are as above. Suppose that $\chi:U\rightarrow X$ is an open embedding and the data

$$\chi^{*}(J),\chi^{*}(kg),\chi^{*}(L^{k}),\chi^{*}(A^{\otimes k})$$

has Property (H). Then there is a holomorphic section $s$ of $L^{k}\rightarrow X$ with $L^{2,\sharp}$ norm at most $(11/10)(2\pi)^{n/2}$ and with $|s(x)|\geq 1/4$ at all points $x$ a distance (in the scaled metric) less than $(4K_{1})^{-1}$ from $\chi(u_{*})$.