The weak-mixing Poisson conjecture for ASL-invariant point processes

Let $\Lambda$ be an $\operatorname{ASL}_d(\mathbb R)$-invariant point process with distribution $\mu$. Let $\mathcal{M}(\mathbb R^d)$ denote the space on which the point-process distribution is defined, and suppose that

$$(\mathcal{M}(\mathbb R^d),\mu)$$

is weakly mixing under the action of $\mathbb R^d$. A weak-mixing Poisson conjecture. Then $\Lambda$ is a Poisson point process. The conjecture is presented as a potentially more approachable analogue of a preceding mixing result, but the source gives no resolution.