Characterization of depth-one Artin–Schreier defect towers

Let $(K,v)$ be a valued field, and let an Artin–Schreier (AS) tower mean a tower $M/K$ formed through Artin–Schreier extensions. Assume that $(K,v)$ is Henselian, perfect, and has no finite limits. The depth-one Artin–Schreier tower conjecture. The tower $M/K$ has depth

$$\operatorname{depth}(M/K,v)=1$$

if and only if $M/K$ is a compositum of Artin–Schreier extensions of $K$. The abstract formulation describes this as the assertion that the composita of linearly disjoint Artin–Schreier defect extensions considered in the paper are the only depth-one Artin–Schreier defect towers; the paper gives examples supporting the conjecture, but no resolution is supplied.