Monadic NIP extension conjecture for modeling FO-limits

A countable signature $\sigma$ and a class $\mathscr C$ of $\sigma$-structures are given. A unary expansion of $\mathscr C$ is obtained by adding unary relation symbols. Monadic NIP extension conjecture. The following properties are equivalent: (1) every FO-convergent sequence of $\sigma$-structures in every unary expansion of $\mathscr C$ has a modeling FO-limit; (2) the class $\mathscr C$ is monadically NIP. The paper establishes the corresponding modeling-limit theorem for monadically stable classes and conjectures this broader monadically NIP characterization, which remains open in the supplied text.