The conjecture that there are no strictly n-dependent fields

For $n\thickspace\geq\thickspace 2$, a theory is strictly $n$-dependent if it is $n$-dependent but not $(n-1)$-dependent. The fields under consideration are in the pure ring language.

No strictly $n$-dependent fields conjecture. There are no strictly $n$-dependent fields for $n\geq 2$.

Equivalently, every $n$-dependent field is dependent. The conjecture is motivated by known results including Artin–Schreier closedness of infinite $n$-dependent fields and the failure of $n$-dependence for non-separable PAC fields. The supplied text gives no resolution of the conjecture.