The nef-canonical-bundle conjecture on semi-orthogonal decompositions

Let $X$ be a smooth projective variety. Let $K_X$ be its canonical bundle and let $h^0(K_X)$ denote the dimension of its global sections. A line bundle is nef if it has nonnegative degree on every curve. Nef-canonical-bundle conjecture. If $K_X$ is nef and

$$h^0(K_X)>0,$$

then $X$ admits no non-trivial semi-orthogonal decomposition. This is presented as a conjecture known among experts; the supplied source gives no resolution or partial status beyond the motivation from semi-orthogonal decompositions and canonical divisors.