Quantum hyperbolic asymptotics and Dehn-filling compatibility conjecture

Let $M$ be a cusped manifold, define

$${\rm R}(M):= {\rm CS}(M) + i\ {\rm Vol}(M) \quad {\rm mod}(\pi^2\mathbb{Z}),$$

and let $H_N(M)$ denote the proposed quantum hyperbolic invariant. Here ${\rm CS}(M)$ and ${\rm Vol}(M)$ are respectively the metric Chern–Simons invariant and hyperbolic volume of $M$. Quantum hyperbolic asymptotics and Dehn-filling compatibility conjecture. There exist $C \in \mathbb{C}^*$ and $D \in \mathbb{C}$ such that

$$H_N(M)^{2N} = \left[ CN^{D}\exp\left( \frac{N\ {\rm R}(M)}{i\pi}\right)\left(1 + \mathcal{O}(1/N)\right) \right]^{2N}.$$

Moreover, if $L$ is a hyperbolic link in $S^3$ and $M=S^3\setminus L$, then

$$H_N(S^3,L,\rho_0) \equiv_N \pm H_N(M).$$

The source presents these assertions as a geometric generalization of the volume conjecture, but notes technical issues concerning the definition and invariance of $H_N(M)$. The supplied parser gives no resolution status.