Orthogonality conjecture for the bimodule summands of a tilted algebra

Let $C$ be a tilted algebra, and let $E=\operatorname{Ext}_{C}^{2}(DC,C)$. Regard $E$ as a $C$-$C$-bimodule and decompose it into indecomposable summands. Orthogonality conjecture. The indecomposable summands of $E$ as a $C$-$C$-bimodule are pairwise orthogonal bricks. This claim describes the structure of the extension bimodule associated with a tilted algebra; the supplied text does not state whether it has been proved or refuted.