Tameness of all Ulam expansions

Let $(a,b)$ be coprime, let $\mathcal{U}_{a,b}$ denote the expansion of $(\mathbb{N},+,0,1)$ by the associated Ulam predicate, and let $\operatorname{Th}(\mathcal{U}_{a,b})$ be its theory. Tameness of all Ulam expansions. For every coprime $(a,b)$, the theory $\operatorname{Th}(\mathcal{U}_{a,b})$ is NIP and does not interpret $(\mathbb{N},+,\times)$. In particular, all expansions $(\mathbb{N},+,\mathrm{U}_{a,b})$ are model-theoretically tame in the sense of classification theory. This asks whether the tameness established under strong rigidity extends to every coprime parameter pair; the source presents it as an open conjecture.