The Archimedean characterization conjecture for PVMDs

Let $D$ be a Prüfer $v$-multiplication domain (PVMD). It is Archimedean if

$$\bigcap_{n=1}^{\infty}(x^n)=(0)$$

for every nonunit $x\in D$.

Archimedean characterization conjecture. $D$ is completely integrally closed if and only if $D$ is Archimedean.

A completely integrally closed domain is known to be Archimedean, but the converse is not known even for PVMDs (and the paper notes that the conjecture is regarded as unlikely). Producing a counterexample would therefore disprove the proposed characterization.