The instability-gap conjecture for generic area-preserving twist diffeomorphisms

Let $\Delta_0$ and $\Delta_1$ denote the instability quantities associated with an area-preserving twist diffeomorphism, and let $V$ be a $C^2$ potential. Instability-gap conjecture. For a generic $C^2$ area-preserving twist diffeomorphism,

$$\Delta_1 \geq \Delta_0^2.$$

This conjecture proposes a quantitative relation between the two measures of instability; the supplied text gives no resolution.