The Katetov order is a way of comparing ideals on infinite sets by asking whether one ideal can be mapped into another via a finite-to-one function. For ideals built from uncountable product spaces, called coordinate ideals, recent work reveals that the behavior of dense subsets within those spaces plays a surprisingly strong and previously underappreciated role in determining where an ideal sits in the Katetov ordering. The open problem is to precisely characterize when two uncountable coordinate ideals are Katetov-equivalent or Katetov-comparable, specifically by identifying which dense-set properties are necessary and sufficient rather than merely sufficient as currently known.