The minimality conjecture for indecomposable derived categories

Let $X$ be a smooth projective variety. Assume that the canonical bundle $K_X$ is nef and effective. A minimality conjecture for indecomposable derived categories asserts that $D(X)$ has no nontrivial semi-orthogonal decompositions. This conjecture concerns the expected relationship between minimal-model geometry and indecomposability of derived categories; it was previously stated in related forms, but its resolution is not indicated here.