Thurston's indecomposable-implies-geometric conjecture

Let $M^{3}$ be a closed, prime, atoroidal $3$-manifold. A locally homogeneous Riemannian metric is a Riemannian metric such that for any two points $p$ and $q$ there is an isometry from a neighborhood of $p$ to a neighborhood of $q$ carrying $p$ to $q$. Indecomposable-implies-geometric conjecture. The manifold $M^{3}$ admits a locally homogeneous Riemannian metric. This is an explicitly stated special case of the geometric decomposition conjecture. The paper says that its main result will prove this conjecture and generalizations for a large class of manifolds, while also stating that it remains far from proved in general at the point of the source.