The complement conjecture for terminal threefold contractions

Let $f\colon X\to Z\ni o$ be a contraction from a threefold with only terminal singularities such that $-K_X$ is $f$-nef and $f$-big. An $n$-complement of $K_X$ is a complement with index $n$. Complement-index conjecture. Near the fiber over $o$, the canonical divisor $K_X$ is $1$-, $2$-, $3$-, $4$-, or $6$-complementary. The source presents this as a more realistic alternative to Reid's general elephant conjecture; no resolution status is supplied.