The so(3) volume conjecture for knots and links

Let $L$ be a knot or link. For a split link with $s$ split components, normalize the colored Jones invariant by dividing by the unnormalized invariant of the $s$-fold unlink; denote the resulting invariant by $J_N(L)$. Let $\mathrm{Vol}(L)$ denote the simplicial volume of the link complement. In the limit below, $N$ ranges over the odd positive integers.

so(3) volume conjecture. For all knots and links $L$,

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

The odd-color modification is motivated by failures for split links and Whitehead chains; the source says that this conjecture still stands a chance to hold for all knots and links, but supplies no resolution.