NIP preservation for the completion and original structure

Let $(R,<,+)$ be a dense archimedean ordered abelian group, let ${\mathscr{R}}$ be an expansion of it, and let ${\mathscr{R}}^{\square}$ be the completion structure used in the paper. Completion NIP conjecture. If ${\mathscr{R}}$ is NIP, then the pair $({\mathscr{R}}^{\square},{\mathscr{R}})$ is NIP. This would reduce the study of NIP expansions of dense archimedean ordered groups to NIP expansions of $(\mathbb{R},<,+)$; the paper notes that the conjecture likely requires tools beyond those currently available.