Solvability conjecture for arithmetic Kac–Witt algebras in composite dimension

Let $n$ be the dimension parameter, let $G$ be the group indexing the choices of $\sigma$, and let $\mathrm{KW}_{b,\sigma}^{\mathscr{A}}(\xi)$ denote the corresponding arithmetic Kac–Witt algebra. Solvability conjecture. If $n$ is composite, then there is at least one $\sigma\in G$ such that

$$\mathrm{KW}_{b,\sigma}^{\mathscr{A}}(\xi)$$

is solvable.

This contrasts with the preceding result that the Jackson subalgebra is non-solvable when $n=p>2$ is prime and $b\neq 0$. The supplied text does not state whether the composite-dimensional claim has been proved or disproved.