Hyperbolicity conjecture for cylinder renormalization

Let $\overline{\Theta}$ be the parameter space of the cylinder renormalization considered in the source, and let $\mathcal{R}_{\operatorname{cyl}}$ denote a cylinder renormalization operator. Cylinder renormalization hyperbolicity conjecture. There is a hyperbolic cylinder renormalization operator $\mathcal{R}_{\operatorname{cyl}}$ with one-dimensional unstable manifolds for all parameters in $\overline{\Theta}$. This would extend the known hyperbolicity results for related Pacman/Siegel renormalization to the cylinder setting; the source does not state a resolution.