Genericity conjecture for the generalized Liouville sequence

Assume $b_k=a_k^2$, with the integers $a_k$ pairwise relatively prime, and define

$$\delta_n:=\left|\{k\geq 1:a_k\text{ divides }n\}\right|,\qquad \pi_n:=(-1)^{\delta_n}.$$

Let $\Sigma$ denote the parameter from the preceding construction, and let $\beta$ be the probability measure defined there. A sequence is generic for $\beta$ if its empirical distributions under the shift converge to $\beta$. Genericity conjecture. When

$$\Sigma=\infty,$$

the sequence $\pi$ is generic for $\beta$. Together with the paper's theorem relating the Chowla property and genericity, this would imply the Chowla conjecture; the source gives no resolution.