Mousavand–Paquette conjecture on finite-dimensional bricks and generic bricks

Let $A$ be a finite dimensional algebra over an algebraically closed field. A brick is an $A$-module whose endomorphism ring is a division ring, and a generic module is an indecomposable $A$-module of infinite length having finite length over its endomorphism ring. Mousavand–Paquette conjecture. The following statements are equivalent:

1. There are infinitely many non-isomorphic finite dimensional bricks.
2. There are infinitely many non-isomorphic finite dimensional bricks of the same dimension.
3. There exists a generic brick.

The equivalence of (2) and (3) is known for tame algebras, while the full equivalence is proved in the paper under the assumption that the Krull–Gabriel dimension of $A$ is defined; the conjecture remains open in general.