But when, exactly, may one wipe over the feet? A person may do so only after putting on fabric socks or leather socks.

Fabric socks (jawrab, pl. jawārib) are those made of cotton, wool, or similar materials.
Leather socks (khuff, pl. khuffayn) are those made of leather or anything comparable.
Wiping over either type is permissible, but only when four conditions are satisfied.

First condition – ritual purity of the socks themselves: the khuffayn or jawārib must be pure. If they are fashioned from inherently impure leather, wiping over them is invalid, for whatever is impure can never be purified no matter how much one wipes or washes it. If, on the other hand, they have merely become contaminated, it is already understood that a person may not pray in them; therefore, he does not wipe over them.

Second condition – having put them on after a water-based ablution: if someone puts them on after performing tayammum, he may not wipe over them. Thus, if a traveler dons socks after attaining purity through tayammum and later reaches a town, he may not avail himself of wiping, because he put them on after a tayammum whose scope concerns only the face and hands and has nothing to do with the feet. This condition is drawn from the Prophet’s statement to al-Mughīrah ibn Shu‘bah: “I put them on when my feet were clean.”

Third condition – that the wiping pertain to minor ritual impurity, i.e., to wuḍū’; whereas