Corollary 8. The canonical orders of the noncanonical varieties in Lemma 6 are uniformly bounded.

Choose a smooth projective resolution u:W→X exhibiting a negative ordinary discrepancy. Its canonical divisor satisfies K_W=u^*K_X+E∼_ E, where E is exceptional with a negative coefficient. By Lemma 7, K_W is not pseudo-effective. The uniruledness criterion of implies that W is uniruled. Its maximal rationally connected quotient consequently has dimension less than four, and its base is non-uniruled . If that base had positive dimension, the induced rational map from X would contradict Lemma 6(i). Thus W is rationally connected. Apply Proposition 4 directly to (X,0) , with zero nef data. Its hypotheses are precisely klt singularities, K_X∼_ 0 , and a rationally connected smooth resolution, all of which have been checked. Its uniform integer bounds the canonical order.