Full $L^2$-Alexander torsion conjecture for monodromy dilatation

Let $K$ be a fibered oriented knot with monodromy $f$, and normalize its full $L^2$-Alexander torsion so that $\tau^{(2)}(K)(1)=1$. Full $L^2$-Alexander dilatation conjecture. Then

$$\sup\left\{T\in\mathbb{Q}_{\geq 0}\mid \tau^{(2)}(K)(t)\big|_{(0,T)}\text{ is constant}\right\}=\exp(-h(f)),$$

where $h(f)$ is the entropy of the monodromy.

Thus the first transition point of the normalized full $L^2$-Alexander torsion would determine the monodromy dilatation. The source presents this as an open conjecture.