Fractal dimension conjecture for self-similar subsets of rings of integers

Let $K$ be a number field, let $O_K$ be its ring of integers, and let $F\subseteq O_K$ be self-similar with respect to polynomial maps $\phi_i:O_K\to O_K$ of degrees $n_i$ and leading coefficients $a_i$. For a fixed embedding $\rho:K\hookrightarrow\mathbb C$, assume $\operatorname{Norm}(a_i)>1$ when $\phi_i$ is linear, and define the fractal dimension by the real number $s$ satisfying

$$\sum_{i=1}^n \operatorname{Norm}(a_i)^{-s/n_i}=1.$$

Fractal-dimension conjecture. The above notion of fractal dimension for self-similar subsets of $O_K$ is well-defined and well-behaved with respect to inclusion: fractal dimension is independent of the choice of self-similarities and compatible with inclusion of self-similar subsets.

This generalizes the stated integer and Gaussian-integer setting, where dimension is asserted to be well-defined and monotone under inclusion. The source does not state whether the number-field version has been proved.