The double-limit volume conjecture for cusped manifolds

Let $M$ be a cusped manifold, and let $(W_n,L_n,\rho_n)$ be a sequence of compact hyperbolic Dehn fillings of $M$ converging to $M$, with $L_n$ the link of short simple geodesics forming the cores of the fillings and $\rho_n$ the holonomy of $W_n$. Let $H_N(W_n,L_n,\rho_n)$ be the corresponding quantum hyperbolic invariant and ${\rm R}(M)$ the complex volume of $M$. Then the double-limit volume conjecture. As $n,N\to\infty$, the dominant term of the asymptotic expansion of

$$\bigl(H_N(W_n,L_n,\rho_n)\bigr)^N$$

is

$$\exp\left(\frac{N^2}{2i\pi}{\rm R}(M)\right),$$

up to multiplication by integer powers of $\exp(i\pi/12)$. This proposal is obtained from the expected limits ${\rm R}(W_n,\rho_n)\to{\rm R}(M)$ and, for fixed $N$, $H_N(W_n,L_n,\rho_n)\to H_N(M)$; the source presents it as a consequence of taking a double limit, without asserting a resolution.