The quantum dilogarithmic scissors-congruence conjecture

Let $M$ be a weakly-gentle cusped manifold, and let $H_N(M)$ be its quantum dilogarithmic invariant. Let $\mathfrak c_{\mathcal I_{fc}}(M)$ denote its ${\mathcal I}_{fc}$-scissors congruence class. For sequences $(W_n,L_n,\rho_n)$ of compact hyperbolic $3$-manifolds converging geometrically to a cusped manifold, let $H_N(W_n,L_n,\rho_n)$ be the corresponding quantum invariant. The dominant term of the asymptotic expansion of $H_N(M)$ as $N\to+\infty$ should depend only on $\mathfrak c_{\mathcal I_{fc}}(M)$; similarly, the dominant term of $H_N(W_n,L_n,\rho_n)$ when both $N$ and $n$ tend to $+\infty$ should depend only on the corresponding scissors congruence data. This conjecture is presented as a weaker form of the proposed Volume Conjecture and is motivated by the structural coincidence between the classical and quantum invariants. Its resolution status is not specified in the source.