Existence conjecture for generic Y-meshes

Let $S$ be a $Y$-pin with maximal admissible dimension $D(S)$, and let $D$ be a positive integer satisfying $D\leq D(S)$. A $Y$-mesh is $D$-generic when its $D$-fractals have the generic dimensions specified in the source. Existence conjecture. If $D\leq D(S)$, then $D$-generic $D$-dimensional $Y$-meshes of type $S$ exist. This is an existence assertion for generic meshes in every dimension allowed by the type; the source provides no resolution.