Extend strong homogenization to generalized higher-dimensional Sierpiński carpets

Establish whether the strong homogenization result for anisotropic diffusions and the weak convergence of suitably rescaled reflected diffusions on pre-Sierpiński carpets extend to generalized Sierpiński carpets in $\mathbb{R}^d$ for $d\geq 3$.

Background

The paper proves strong homogenization and convergence to Brownian motion for anisotropic diffusions on the standard planar Sierpiński carpet. It explicitly raises the higher-dimensional generalization as unresolved. The authors regard the extension as plausible, but explain that the presence of additional coordinate directions makes the flow-gluing techniques used in the proof substantially more difficult.