Clifford-band width conjecture

Let $M_{p,q}=\mathbf S^p\times\mathbf S^q\times[-1,1]$ be a Clifford band, and let $g$ be a smooth metric on $M_{p,q}$. Clifford-band width conjecture. If

$$\operatorname{sec}(g)\geq1,$$

then

$$\operatorname{width}(M_{p,q},g)\leq\frac{\pi}{2}.$$

This is a proposed higher-dimensional analogue of the positive-sectional-curvature width estimate for overtorical bands; the source gives no resolution of the conjecture.