Positive synthetic Ricci curvature conjecture for orientable Alexandrov spaces

Let $M$ be an orientable Alexandrov space of dimension $n$ without boundary. Assume that a synthetic lower Ricci curvature bound, in the terminology of optimal transport theory, is nonnegative everywhere and positive at at least one point.

Positive synthetic Ricci curvature conjecture. Under these assumptions,

$$H_{n-1}(M;\mathbb R)=0.$$

This would extend the vanishing result proved in the paper for spaces satisfying a stronger positive curvature-dimension condition. The supplied source does not state that the conjecture has been proved or disproved.