The full-dimensional Newhouse lamination conjecture

Let $d$ be the dimension of a parameter space, and consider a $d$-dimensional unfolding of a map with a strong homoclinic tangency. A codimension $2$ Newhouse lamination is a Newhouse lamination of codimension $2$ in this parameter space.

Newhouse lamination conjecture. Every $d$-dimensional unfolding of a map with a strong homoclinic tangency contains a codimension $2$ Newhouse lamination with Hausdorff dimension $d$.

The conjecture proposes that the construction based on one transversal homoclinic intersection extends using all transversal homoclinic intersections, producing laminations that are full-dimensional in the parameter space. The supplied text gives no resolution, so the conjecture remains open.