Detcherry–Kalfagianni–Yang generalized Turaev–Viro volume conjecture for links

Let $L$ be a link in $\mathbb S^3$, and let $v_3$ be the volume of an ideal regular tetrahedron. Then

Detcherry–Kalfagianni–Yang generalized Turaev–Viro volume conjecture.

$$\lim_{\substack{r\to\infty\r\ \operatorname{odd}}}\frac{2\pi}{r}\log\left(TV_r\left(\mathbb S^3\setminus L,e^{\frac{2\pi i}{r}}\right)\right)=v_3\left\|\mathbb S^3\setminus L\right\|.$$

This extends the Turaev–Viro volume conjecture from finite-volume hyperbolic manifolds to complements of arbitrary links, with simplicial volume replacing hyperbolic volume. The source notes that the generalization was proved for knots with zero simplicial volume, but does not resolve the conjecture for all links.