Linear dependence conjecture for Norton algebra vectors

Let $\Gamma=(X,\mathcal R)$ be a distance-regular graph that is $Q$-polynomial with respect to a primitive idempotent $E$. For distinct vertices $x,y\in X$, let $C(x,y)$ and $B(x,y)$ be the vectors appearing in the expression for the Norton algebra product $E\hat{x}\star E\hat{y}$, together with $E\hat{x}+E\hat{y}$. Assume that $\Gamma$ satisfies Assumptions and. The Norton algebra linear-dependence conjecture. The vectors $C(x,y)$, $B(x,y)$, and $E\hat{x}+E\hat{y}$ are linearly dependent. The conjecture concerns the structure of the Norton algebra associated with a $Q$-polynomial distance-regular graph; its status is not determined by the supplied text.