$v$. If $\mu(v,u_1) = 1$, then the $H$-type configuration about $v$ and $u_1$ is of the form $H(7,7;0;s_1,s_2)$; by Claim \[clm:Reducible\] $s_1+s_2 \leq 9$, $|\operatorname{Resp}(u_1)|\leq 9$, and $u_1$ sends charge $\frac{1}{7}$ to $v$ by Rule R\[adj\]. If $\mu(v,u_1) = 2$, then the $\Phi$-type configuration about $v$ and $u_1$ is of the form $\Phi(7,0,7,s)$; by Claim \[clm:Reducible\] $s = 0$, $|\operatorname{Resp}(u_1)|\leq 7$, and $u_1$ sends charge $\frac{1}{7}$ to $v$ by Rule R\[adj\].

*Case : $|\operatorname{Resp}(v)| = 13$.*

By Claim \[clm:Reducible\], the $Y$-type configuration $Y(t_1,t_2,t_3)$ about $v$ is one of $Y(0,6,7)$, $Y(1,6,6)$, $Y(1,5,7)$, $Y(2,4,7)$, or $Y(3,3,7)$. We consider each case separately.

*Case [.]{}: $(t_1,t_2,t_3) = (0,6,7).$*

Let $u_1$ be the vertex in $N_3(v)$ at distance 1 from $v$. If $\mu(v,u_1) = 1$, then the $H$-type configuration about $v$ and $u_1$ is of the form $H(6,7;0;s_1,s_2)$; by Claim \[clm:Reducible\] $s_1+s_2 \leq 9$, $|\operatorname{Resp}(u_1)|\leq 9$, and $u_1$ sends charge $\frac{1}{14}$ to $v$ by Rule R\[near\]. If $\mu(v,u_1) = 2$, then the $\Phi$-type configuration about $v$ and $u_1$ is of the form $\Phi(6,0,7,s)$ or $\Phi(7,0,6,s)$; by Claim \[clm:Reducible\] $s = 0$, $|\operatorname{Resp}(u_1)|\leq 7$, and $u_1$ sends charge $\frac{1}{14}$ to $v$ by Rule R\[near\].

*Case [.]{}: $(t_1,t_2,t_3) = (1,6,6).$*

Let $u_1$ be the vertex in $N_3(v)$ 