The field-type conjecture for NIP expansions by closed sets

Let ${\mathscr{R}}$ be an NIP expansion of $(\mathbb{R},<,+)$ by closed subsets of Euclidean space. Call ${\mathscr{R}}$ field-type when it satisfies condition (1): there is a nonempty open interval $I$ and continuous definable operations $\oplus,\otimes:I^2\to I$ such that $(I,<,\oplus,\otimes)$ is an ordered field isomorphic to $(\mathbb{R},<,+,\times)$. Field-type conjecture. If ${\mathscr{R}}$ interprets an infinite field, then ${\mathscr{R}}$ is field-type. The conjecture concerns whether interpreting an infinite field in this tame setting necessarily yields a definable real field on an interval; the paper proves several special cases and notes that the formulation can be changed from interprets to defines under definable selection.