Irreducibility conjecture for the degree-two nilpotency series of finite simple groups

Let $G$ be a finite group. Define $R_2(G,s)$ as the degree-two nilpotency series associated with $G$, and let

$$\mathcal{R}=\left\{\sum_{n\geq 0}\frac{a_n}{n^s}:a_n\in\mathbb{Z},\ a_n\neq 0\text{ for only finitely many }n\right\}.$$

Irreducibility conjecture. If $G$ is a finite simple group, then $R_2(G,s)$ is irreducible in $\mathcal{R}$. The examples in the paper show irreducibility for particular finite simple groups, but the assertion for all finite simple groups remains unresolved in the supplied text.