Dynamic comparison implies strict comparison for transformation group C*-algebras

Let $(X,h)$ be a minimal dynamical system, and assume that $(X,h)$ has the dynamic comparison property. Write $C^{*}({\mathbb Z},X,h)$ for the transformation group $C^{*}$-algebra associated to the action generated by $h$. Dynamic comparison conjecture. Then $C^{*}({\mathbb Z},X,h)$ has strict comparison of positive elements. This is proposed as a topological analogue of strict comparison for positive elements in $C^{*}$-algebras; the source presents it as a suggested principle rather than an established result.