The maximal self-orthogonal conjecture for Wakamatsu tilting modules

Let $\Lambda$ be an artin algebra. A module is self-orthogonal if all its positive self-extension groups vanish, and maximal self-orthogonal if it cannot be enlarged by a non-isomorphic indecomposable direct summand while remaining self-orthogonal.

Maximal self-orthogonal conjecture. Every Wakamatsu tilting module is maximal self-orthogonal.

The conjecture predicts maximality of Wakamatsu tilting modules among self-orthogonal modules. The paper notes that maximal self-orthogonal modules and Wakamatsu tilting modules need not coincide in general, so the proposed implication remains open.