Braunfeld's monadic NIP orbit-growth conjecture

Let $c9$-categorical mean categorical in every infinite cardinality, let $c1$-categorical structures be countable here, and for a countable $c9$-categorical structure $c4$ let $u_n(c4)$ denote the number of orbits of $c0 goperatorname{Aut}(c4)$ on $n$-element subsets of $c4$. A structure is monadically NIP if every expansion by unary predicates is NIP.

Braunfeld's monadic NIP orbit-growth conjecture. For a countable $c9$-categorical structure $c4$, $c4$ is monadically NIP if and only if

$$u_n(c4)<c^n$$

for some $c\tilde{}bb R$.

This conjecture is cited from Braunfeld's work as the reason no orbit-growth characterization of monadically NIP structures is currently known. The paper proves the analogous closure result for model-complete cores, but does not resolve this characterization.