Generalised Nakayama conjecture

Let $A$ be a finite-dimensional $K$-algebra, and let $S$ be a simple $A$-module. Write $\operatorname{grade} S$ for the grade of $S$. Generalised Nakayama conjecture. For every simple $A$-module $S$, one has

$$\operatorname{grade} S<\infty.$$

This is one of the classical open homological conjectures for finite-dimensional algebras. It implies the Nakayama conjecture and is itself a consequence of the finitistic dimension conjecture.