Hubbard's existence conjecture for type-3 parameters of the complex Hénon map

Let $(a,c)\in\mathcal{H}^{\mathbb{C}}\cap\mathbb{R}^2$ be a real parameter in the hyperbolic locus of the complex Hénon map. Such a parameter is of type-1 if $(a,c)\in\mathcal{H}^{\mathbb{R}}$, of type-2 if $K_{a,c}^{\mathbb{R}}=\emptyset$, and of type-3 otherwise. Hubbard's conjecture. There exists a parameter value of type-3. The paper states that this conjecture is later proved, so the conjecture is solved.