Saito's finiteness conjecture for opposite series of hyperbolic groups

Let $G$ be a group with a finite generating set $S$, and let $\Omega(G,S)$ be Saito's set associated with the word-growth series of $(G,S)$. Saito's conjecture. If $G$ is a word hyperbolic group, then

$$\Omega(G,S)\text{ is finite}.$$

Saito's theory relates $\Omega(G,S)$ to the accumulation points of the normalized polynomials associated with the word-growth series. The conjecture is still open.