Hirasawa–Murasugi metabelian twisted Alexander polynomial conjecture

Let $K$ be a knot with knot group $G(K)$, and suppose there is a homomorphism $f:G(K)\twoheadrightarrow M(n\mid p,k)$. Let $N=\langle s\rangle=\{1,s,s^2,\ldots,s^{n-1}\}$ and let $\widehat N$ be the set of right cosets of $M(n\mid p,k)$ modulo $N$. The induced permutation representation gives a representation

$$\rho:G(K)\longrightarrow GL(p^k,\mathbb Z),$$

and assume that a meridian generator $x$ satisfies $f(x)=s$. Write $\widetilde{\Delta}_{\rho,K}(t)$ for the twisted Alexander polynomial associated to $\rho$. Hirasawa–Murasugi's conjecture. The polynomial has the form

$$\widetilde{\Delta}_{\rho,K}(t)=\left[\frac{\Delta_K(t)}{1-t}\right]\varphi(t),$$

where $\varphi(t)$ is an integer polynomial in $t^n$. This predicts a cyclotomic pattern for twisted Alexander polynomials arising from metabelian quotient representations; the source proposes it in the general metabelian setting, and no resolution is supplied there.