Agol–Storm–Thurston scalar curvature and volume entropy conjecture

Let $(M,g)$ be a closed Riemannian $3$-manifold, let $R_g$ denote its scalar curvature, and let $h(g)$ denote its volume entropy. Agol–Storm–Thurston conjecture. If

$$R_g \geq -6,$$

then

$$h(g)\leq 2.$$

This conjecture proposes a direct relation between scalar curvature and volume entropy in dimension three. The paper's abstract states that its construction gives counterexamples, so the conjecture is refuted.