5 problems

Strong $b5$-lc complement conjecture. For every $0<b5$ and $d$, there exists a finite set $a9_{b5,d}$ of positive integers such that every such pair has an $(b5,n)$-complement over…

Weak $b5$-lc complement conjecture. For every $0<b4$ and $d$, there exist a finite set $a9_{b4,d,91b}$ of positive integers and $0<b5$ such that every such pair is $(b5,n)$-complem…

$a$-$n$-complements conjecture. Under the additional assumption that $(X/Z\ni o,B)$ has an $a$-lc over $o$ $\mathbb R$-complement, the cited complement theorems should yield an $a$…

Boundedness of lc index conjecture. There exist a finite subset $\Gamma(d)\subseteq\Gamma$ and a positive integer $I=I(d,\Gamma)$, depending only on $d$ and $\Gamma$, such that eve…

Existence and boundedness of $n$-complements conjecture. The cited theorems should hold without assuming that $X/Z\ni o$ has wFt. The connectedness assumption on $X_o$ may instead…