Index-one conjecture for the biharmonic map from the generalised Clifford torus

Let $\mathbb S^{l}(\frac{1}{2})\times\mathbb S^{l}(\frac{1}{2})$ be the generalised Clifford torus, viewed as a submanifold of $\mathbb S^{2l+2}$, and consider the associated biharmonic map into $\mathbb S^{2l+2}$. Generalised Clifford torus index conjecture. The biharmonic map constructed from the generalised Clifford torus has index $1$. This would determine the precise index in this family; the surrounding results provide lower bounds for indices of biharmonic maps, but the supplied text gives no resolution of this claim.