Conjectured convergence of electrostatic energy for Apollonian gaskets

Let $\mathcal C_T$ be the set of gasket points used in the source, let $d(p,q)$ denote the distance between points, and define the normalized electrostatic energy by

$$G(T):=\frac{1}{T^{2\delta}}\sum_{\substack{p,q\in\mathcal C_T\p\neq q}}\frac{1}{d(p,q)}.$$

Electrostatic energy convergence conjecture. There exists a constant $b>0$ such that

$$\lim_{T\rightarrow\infty}G(T)=b.$$

The normalization is chosen to match the electrostatic energy of an array of electrons up to the factor $T^{-2\delta}$. Numerical experiments suggest convergence to a positive constant, but no proof or resolution is supplied here.