Generalized Chen–Yang volume conjecture for 3-manifolds

Let $M$ be a compact orientable 3-manifold with empty or toroidal boundary. Define

$$LTV(M):=\limsup_{r\rightarrow\infty,\ r\ \operatorname{odd}}\frac{2\pi}{r}\log\lvert TV_r(M)\rvert,$$

where $r$ runs over all odd integers, and let $\operatorname{Vol}(M)$ be the simplicial volume, equivalently the sum of the volumes of the hyperbolic pieces in the geometric decomposition of $M$. The generalized Chen–Yang volume conjecture.

$$LTV(M)=\operatorname{Vol}(M).$$

This conjecture extends the finite-volume hyperbolic case to all compact orientable 3-manifolds with empty or toroidal boundary, using the geometric decomposition into hyperbolic and Seifert-fibered pieces. The source gives no resolution of the general statement.