Minimal models in numerical dimension one

We resolve the numerical-dimension-one case of the minimal-model conjecture for smooth connected complex projective varieties of dimension at least three. If K${}_X$ is pseudo-effective and ${\kappa }_{\sigma }(X,K_X)=1$, with κ${}_{\sigma }$ defined by section growth with a fixed ample twist, then X admits a projective ℚ-factorial terminal minimal model.