Chen–Xi's derived-equivalence conjecture for Morita algebras

Let $A$ and $B$ be finite-dimensional algebras over a field $K$, with all modules finitely generated right modules. The algebras are derived equivalent if their bounded derived categories of finitely generated modules are equivalent. An algebra is a Morita algebra if it has dominant dimension at least two and a minimal faithful projective-injective right module $eA$ such that $eAe$ is selfinjective.

Chen–Xi's conjecture. Suppose two algebras $A$ and $B$ are derived equivalent. If $A$ is a Morita algebra and the dominant dimension of $B$ is at least two, then $B$ is also a Morita algebra.

The conjecture concerns whether the Morita-algebra property is preserved in this one-sided form under derived equivalence. The paper's abstract states that the authors construct a counterexample, so the conjecture is refuted.