Borisov–Alexeev boundedness conjecture for log Fano varieties

Let $\epsilon\in (0,1]$ and $d\in {\mathbb Z}_{\geq 1}$. A log variety $X$ has minimal log discrepancy $a(X)$, and $-K_X$ is ample when $X$ is log Fano.

Borisov–Alexeev boundedness conjecture. Log varieties $X$ with $-K_X$ ample, $a(X)\geq \epsilon$, and $\dim(X)=d$ form a bounded family.

This is a boundedness statement for log Fano varieties with fixed dimension and a uniform lower bound on minimal log discrepancies. The source presents it as a conjecture; its resolution is not supplied here.