Completeness conjecture for the construction of homogeneous finite-dimensional permutation structures

The construction referred to in the source starts with a finite distributive lattice $\Lambda$, takes a well-equipped lift of the class of finite $\Lambda$-ultrametric spaces, and forms its Fraïssé limit, which is interdefinable with a finite-dimensional permutation structure.

Construction completeness conjecture. This construction produces all homogeneous finite-dimensional permutation structures.

The source presents this as the conjectural classification motivating the later chapters and gives no resolution.