Rigidity conjecture for Lipschitz equivalence of self-similar sets

Let ${\boldsymbol{\rho}}=(\rho_1,\ldots,\rho_m)$ be a contraction vector such that $\operatorname{rank}\langle {\boldsymbol{\rho}}\rangle=m$, and let ${\boldsymbol{\tau}}=(\tau_1,\ldots,\tau_n)$ be another contraction vector. Let ${\mathcal D}({\boldsymbol{\rho}})$ and ${\mathcal D}({\boldsymbol{\tau}})$ denote the corresponding dust-like self-similar sets, and say that ${\boldsymbol{\tau}}$ is derived from ${\boldsymbol{\rho}}$ in the sense used in the source. Rigidity conjecture. ${\mathcal D}({\boldsymbol{\rho}})$ and ${\mathcal D}({\boldsymbol{\tau}})$ are Lipschitz equivalent if and only if ${\boldsymbol{\tau}}$ is derived from ${\boldsymbol{\rho}}$. This extends the full-rank characterization to the case where the two contraction vectors may have different lengths. The source states that the question is open in this generality, while the cited work completely answers a related question; the conjecture itself is not marked as resolved.