Are feet and carpets defiled by invisible cat urine, and is the hand defiled by touching wet impurity when no trace of it is visible on it?

The earth and what is connected to it become pure by dryness according to many scholars. So, if the place where a cat urinated or its impurity dries up, it is judged to be pure. The fundamental principle regarding places is purity. And unless there is absolute certainty that a place has been contaminated by impurity, the original state is purity. The transfer of impurity from a dry, contaminated spot to a wet or damp one is a matter of scholarly disagreement. For someone afflicted with obsessive doubts, they may adopt the opinion that impurity does not transfer in this case.