Existence of exponential mixing skew-product semiflows without constant stable-leaf return times

Let an expanding semiflow be given together with its stable leaves and an original flow to which a skew-product model may be semiconjugated. Exponential mixing skew-product conjecture. There exists an exponentially mixing skew-product semiflow built over the expanding semiflow, with a roof function that is non-constant on stable leaves, and semiconjugated to the original flow. This would remove the apparent need for constant return times along stable leaves and hence for smoothness of the strong stable foliation in the existing construction; whether such a model can always be obtained remains open.