The pure-field NIPn conjecture

For $n\geqslant 2$, a pure field is NIP$_n$ if no formula in its language has the independence property of order $n$, and it is strictly NIP$_n$ if it is NIP$_n$ and has the independence property of order $n-1$.

Pure-field NIP$_n$ conjecture. For every $n\geqslant 2$, no strictly NIP$_n$ pure fields exist; equivalently, a pure field is NIP$_n$ if and only if it is NIP.

The conjecture concerns pure fields; the surrounding text notes that arbitrary additional structure can destroy it, while natural expansions such as valuations or distinguished automorphisms are expected to preserve the phenomenon. No resolution is supplied.