What are the conditions for wiping over the leather socks (khuffayn), along with the evidence for that?

There are four conditions for wiping over the khuff (leather socks) or socks:

1. One must have worn them while in a state of ritual purity (tahara).

2. The khuff or socks must be ritually pure (tahir).

3. The wiping must be for a minor ritual impurity (minor hadath), not for janaba (major ritual impurity) or anything that necessitates a ritual bath (ghusl).

4. The wiping must be within the time limit prescribed by Islamic law: one day and one night for a resident, and three days and three nights for a traveler. The duration begins from the first wiping after an impurity. If the duration expires, the preponderant opinion is that the purity is not invalidated by the end of the duration itself, but by the occurrence of another purity-nullifying factor.