Removable-poles conjecture for generalized Sierpinski carpets

Let a generalized Sierpinski carpet have self-similar, possibly graph-directed, structures yielding the same Laplacian operator. Let $d_k$ denote the relevant dimensions, with $k=1,\ldots,d-1$, and let $d_w$ be the walk dimension. The possible poles under consideration have real part $2d_k/d_w$. Removable-poles conjecture. These possible poles should be removable singularities because different self-similar structures can yield the same Laplacian operator. The claim applies to the usual Neumann Laplacian when the zero eigenvalue is excluded; for the Dirichlet Laplacian, the boundary dimension should instead affect the spectral asymptotics. This conjecture concerns whether the apparent intermediate-dimensional pole sequences reflect genuine spectral singularities or redundancy in the self-similar descriptions.