The NIPn Fields Conjecture

Let $n\geqslant 2$. A pure field is a field considered only in the language of rings, and a theory is strictly NIP$_n$ when it is NIP$_n$ but has IP$_{n-1}$. The NIP$_n$ Fields Conjecture. For $n\geqslant 2$, strictly NIP$_n$ pure fields do not exist; equivalently, a pure field is NIP$_n$ if and only if it is NIP. This concerns pure fields: adding arbitrary structure can destroy the conclusion, while natural expansions such as valuations or distinguished automorphisms are expected to preserve it. The conjecture is presented as arising from work of Hempel, Chernikov, and others; its status is not specified in the source.