The density conjecture for the family lambda tan z

Let ${\cal F}$ be the holomorphic family defined over ${\bf C}-\{0\}$, and let J-stable maps be the maps whose Julia sets vary stably in this family. The Density Conjecture. The hyperbolic components are open and dense in the J-stable maps. This asks whether hyperbolic dynamics accounts for all open components of J-stability; the paper presents computer evidence in its favor, but the supplied text gives no resolution.