Packing measure formula for regular-polygon self-similar sets

Let $E_r$ be the self-similar set associated with a system of contracting similitudes $\Psi=\{f_1,f_2,\ldots,f_N\}$ satisfying the strong separation condition. Suppose that, for every $i=1,\ldots,N$, $f_i(x)=rx+b_i$, where $r\in(0,\frac{1}{N})$ and $x,b_i\in\mathbb{R}^n$. Let $s(r)$ be the similarity dimension, let $\mu$ denote the natural measure, and suppose that the fixed points of the $N$ similarities are the vertices of an $N$-regular polygon. Then

Regular-polygon packing measure formula. The conjectured packing measure satisfies

$$P^{s(r)}(P_r)=\frac{|B(x_i,1-r)|^{s(r)}}{\mu(B(x_i,1-r))}=\left(2\frac{1-r}{r}\right)^{s(r)}.$$

The claim is presented as the conjectural conclusion of the numerical and algorithmic results preceding it. The supplied text does not indicate whether it has been proved or disproved.