Finite grade for simple modules in the generalized Nakayama conjecture

Prove that every simple module over an arbitrary finite-dimensional algebra has finite grade, thereby resolving the generalized Nakayama conjecture.

Background

The grade of a simple module is the least degree in which its Ext group with the algebra is nonzero. The paper notes that the generalized Nakayama conjecture asserts finiteness of this grade for every simple module and remains unresolved in general, although the authors prove the property for Iwanaga–Gorenstein algebras.