Chen–Yang's Turaev–Viro volume conjecture

Let $M$ be a hyperbolic $3$-manifold, either closed, with cusps, or compact with totally geodesic boundary. Chen–Yang's Turaev–Viro volume conjecture. As $r$ varies along the odd natural numbers, one has

$$\lim_{r\rightarrow\infty}\frac{2\pi}{r}\log\left|TV_{r}(M,t)\right|=\operatorname{Vol}(M).$$

This conjecture proposes that the exponential growth of the Turaev–Viro invariant detects the hyperbolic volume. The source presents an asymptotic formula for the Whitehead-link surgery manifolds, confirming the conjecture in that setting.