Conjecture on cyclic extensions with p-rational total field

Let $p$ be a prime and let $m\geq 1$ be an integer coprime to $p$. A number field is $p$-rational when it has the standard $p$-rationality property used in the paper. Cyclic p-rationality conjecture. There exist a totally imaginary number field $K_0$ and a cyclic extension $K/K_0$ of degree $m$ such that $K$ is $p$-rational. This conjecture is introduced as a reduction target for the arithmetic-realization conjecture; the source gives no proof or resolution.