A gap theorem for minimal log discrepancies of noncanonical singularities in dimension three

We show that there exists a positive real number $\delta>0$ such for any normal quasi-projective $\mathbb{Q}$-Gorenstein $3$-fold $X$, if $X$ has worse than canonical singularities, is, the minimal log discrepancy of is less $1$, then not greater $1-\delta$. As applications, we set all non-canonical klt Calabi-Yau $3$-folds are bounded modulo flops, and global indices from above.