Toroidal simplicial-volume conjecture for irreducible link complements

Let $L\subset T^2\times I$ be a link whose complement $(T^2\times I)\setminus L$ is irreducible, and let $J_n^T(L;e^{2\pi i/n})$ be the toroidal colored Jones polynomial evaluated at $e^{2\pi i/n}$. Here $\operatorname{Vol}$ denotes simplicial volume, and $n>0$ ranges over all odd integers.

Toroidal simplicial-volume conjecture.

$$\lim_{n\to\infty}\frac{2\pi}{n}\log\left|J_n^T\left(L;e^{2\pi i/n}\right)\right|=\operatorname{Vol}\bigl((T^2\times I)\setminus L\bigr).$$

This extends the hyperbolic-complement conjecture to irreducible complements by using simplicial volume, which sums the hyperbolic volumes of the hyperbolic JSJ pieces. Its general validity is left open.