Crawley-Boevey's modification of the Second Brauer–Thrall Conjecture

Let $A$ be an artin algebra of infinite representation type. For an $A$-module $M$, its endolength is its length as a module over its endomorphism ring. Brauer–Thrall II. There exists $n\in\mathbb{N}$ such that infinitely many pairwise non-isomorphic indecomposable $A$-modules have endolength $n$ and finite length as $A$-modules. This is a modification of the Second Brauer–Thrall Conjecture suggested by Crawley-Boevey. The supplied text does not state whether this formulation has been resolved, so its status is recorded as open.