Detcherry–Kalfagianni simplicial-volume conjecture for Turaev–Viro invariants

Let $M$ be a compact and orientable $3$-manifold with empty or toroidal boundary. For odd integers $r$, set

$$q=e^{\frac{2\pi \sqrt{-1}}{r}}.$$

Let $v_3\approx 1.0149$ be the volume of a regular ideal tetrahedron, and let $\lVert M\rVert$ denote the simplicial volume of $M$. Detcherry–Kalfagianni simplicial-volume conjecture. The Turaev–Viro invariants satisfy

$$\limsup_{r\rightarrow\infty}\frac{2\pi}{r}\log\lvert \operatorname{TV}_r(M;q)\rvert=v_3\lVert M\rVert.$$

This is a natural extension of the Chen–Yang volume conjecture from hyperbolic manifolds to manifolds that may have non-hyperbolic geometric pieces, replacing hyperbolic volume by simplicial volume. The source presents it as a conjecture and gives no resolution.