Structural conjectures for finitely homogeneous NIP structures

Let $M$ be a finitely homogeneous NIP structure. Structural conjecture. The following hold:

1. The automorphism group $\operatorname{Aut}(M)$ acts oligomorphically on the space of types $S_1(M)$.
2. The structure $M$ is interpretable in a distal, finitely homogeneous structure.
3. There is a structure $M'$ bi-interpretable with $M$ whose theory is quasi-finitely axiomatizable.
4. If $M$ is not distal, then its theory is not finitely axiomatizable.

These assertions are presented as precise goals for the general NIP case, following the paper's discussion of the difficulty of classifying all finitely homogeneous NIP structures. Their status is not resolved in the supplied text.