The non-bidirectionality conjecture for subatomic domain properties

Let the classes of rings in Figure $1$ be the unique factorization domains, atomic domains, semi-atomic domains, almost atomic domains, quasi-atomic domains, Furstenberg domains, semi-Furstenberg domains, almost Furstenberg domains, quasi-Furstenberg domains, not-antimatter domains, and integral domains, with the arrows in Figure $1$ denoting the displayed implications. Non-bidirectionality conjecture. None of the arrows in Figure $1$ are bidirectional. The conjecture concerns whether the displayed hierarchy of subatomic domain properties has any equivalences among its arrows; the supplied text does not state whether it has been resolved.