The BAB conjecture for epsilon-lc Fano varieties

Let $d$ be a natural number and $\epsilon>0$ be a real number. An $\epsilon$-lc Fano variety is a Fano variety of dimension $d$ whose singularities are $\epsilon$-lc.

BAB conjecture. The set of $\epsilon$-lc Fano varieties of dimension $d$ forms a bounded family.

This is a fundamental boundedness question in birational geometry. The conjecture was proved in characteristic zero by Birkar using Shokurov's theory of complements; the positive-characteristic analogue is the subject of the paper.