Silver–Williams conjecture for total twisted Alexander polynomials

Let $K(r)$ be a 2-bridge knot and let $\rho$ be a canonical parabolic representation. Let $\theta(z)$ be the minimal polynomial of the representation parameter $s_r$, let $d=\operatorname{deg}\theta$, and let $D_{\rho(\theta),K(r)}(t)$ denote the total $\rho(\theta)$-twisted Alexander polynomial.

Silver–Williams conjecture.

$$\left|D_{\rho(\theta),K(r)}(1)\right|=2^d$$

and

$$\left|D_{\rho(\theta),K(r)}(-1)\right|=2^dN^2,$$

where $N$ is a non-zero integer.

The conjecture predicts uniform evaluations at $1$ and $-1$ for total twisted Alexander polynomials. It is attributed in the source to D. Silver and S. Williams; no resolution is supplied.