Equality conjecture for the Riesz capacity decay of strictly self-similar fractals

A compact set $A \subset \mathbb{R}^n$ is a strictly self-similar fractal if

$$A=\bigcup_{i=1}^N\varphi_i(A),$$

where $\varphi_i(x)=L_iU_ix+b_i$ with $L_i\in(0,1)$, $U_i$ a unitary matrix, and the sets $\{\varphi_i(A)\}_{i=1}^N$ are disjoint. Let $d>0$ be its Hausdorff dimension, and let $\sigma_d(A)$ denote its constant second-order density. Here $\operatorname{Cap}_p(A)$ is the Riesz $p$-capacity of $A$.

Equality conjecture. If $A$ is a strictly self-similar fractal with dimension $d$, then

$$\lim_{p\nearrow d}\frac{\operatorname{Cap}_p(A)^p}{d-p}=\frac{\mathcal{H}^d(A)}{d\,\sigma_d(A)}.$$

The preceding result gives the corresponding lower bound for strictly self-similar fractals. The conjecture asks whether that lower bound is always sharp; the supplied text does not indicate whether the equality has been proved or disproved.