Two-vertex conjecture for minimal geometrically irreducible algebras

Let $A=KQ/{\mathcal I}$ be a finite-dimensional algebra presented by a quiver with relations. Call $A$ minimal if ${\mathcal I}=0$, or if every generating set of relations satisfies the connectivity and coverage conditions specified in the paper. Assume that $A$ is minimal and geometrically irreducible, and that ${\mathcal I}\ne 0$. Two-vertex conjecture. The quiver $Q$ has at most two vertices. The statement would reduce the classification of nontrivial minimal geometrically irreducible algebras to quivers with at most two vertices; no resolution is supplied in the source context.