Weak-tiling conjecture for SRS tiles

Let $\mathbf{r}=(r_0,\ldots,r_{d-1})\in\mathcal{E}_d$ with $r_0\neq0$, and let $\mathcal{T}_{\mathbf{r}}(\mathbf{x})$ be the SRS tile associated with $\mathbf{x}\in\mathbb{Z}^d$.

SRS weak-tiling conjecture. The collection

$$\{\mathcal{T}_{\mathbf{r}}(\mathbf{x}):\mathbf{x}\in\mathbb{Z}^d\}$$

is a weak tiling of $\mathbb{R}^d$.

This is presented as a stronger form of the possible weak $m$-tiling property for SRS tiles and includes the Pisot conjecture for beta-tiles as a special case. The survey gives no resolution.