The geometric volume conjecture for SO(3)-knot states

Let $K$ be a knot in $S^3$. The geometric quantized space for the $SO(3)$-Witten–Chern–Simons theory of the torus is the alternating subspace

$$\mathcal{H}^{alt}_{r+\frac{1}{2}}(j,\delta)$$

of holomorphic sections of $L^r\otimes L^{\frac{1}{2}}\otimes\delta$ over the $SU(2)$-character variety of the torus. Let $Z'_r(S^3\backslash K)\in\mathcal{H}^{alt}_{r+\frac{1}{2}}(j,\delta)$ be the $r$-th $SO(3)$-knot state, and let $\operatorname{vol}(S^3\backslash K)$ be the simplicial volume of its complement. The geometric volume conjecture.

$$\lim_{r\rightarrow+\infty}\frac{\pi}{r}\log\left\|Z'_r(S^3\backslash K)\right\|^2_{r+\frac{1}{2}}=\operatorname{vol}(S^3\backslash K).$$

This is presented as a geometric version of the volume conjecture, interpreting the left-hand side as a form of quantum complexity. Its resolution is not given in the source.