Strong reinforcement conjecture for simultaneous drawing urns

Let $d\geq 2$ and consider the simultaneous drawing urn process with reinforcement weights $(w_i)_{i\geq 0}$. Let $A$ be the event that there is a time after which all balls drawn from the urn have the same colour, and let

$$s_{\infty}:=\sum_{i=0}^{\infty}\frac{1}{w_i}.$$

Strong reinforcement conjecture. If $s_{\infty}<\infty$, then

$$\mathbb{P}[A]=1.$$

For the ordinary urn process ($d=1$), Davis's result establishes the analogous zero-one law: almost-sure eventual fixation occurs exactly when the strong reinforcement hypothesis holds. The conjecture asks whether the almost-sure fixation conclusion remains valid for simultaneous drawing with every $d\geq 2$; the supplied source gives no resolution.