The limsup volume conjecture for non-splittable links

Let $L$ be a non-splittable link, let $J_N(L)$ denote its normalized $N$-colored Jones polynomial, and let $\mathrm{Vol}(L)$ be $v_3$ times the simplicial volume of $\mathbb{S}^3-L$, where $v_3$ is the volume of the regular ideal hyperbolic tetrahedron.

Limsup volume conjecture. For every non-splittable link $L$,

$$\limsup_{N\to\infty}\frac{2\pi}{N}\log\left|J_N(L)\left(e^{\frac{2\pi i}{N}}\right)\right|=\mathrm{Vol}(L).$$

The main theorem shows that the original volume conjecture can fail for non-splittable links, motivating this weaker formulation; its general validity remains open.