What types of ritual impurity permit wiping over the leather socks?

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Wiping is exclusively permissible following the occurrence of minor ritual impurity (hadath asghar). Wiping is not permissible in a state of major ritual impurity (janabah), nor for obligatory or recommended ritual ghusl (full bath). This ruling is established without known disagreement. Safwan ibn Assal al-Muradi narrated that the Prophet (peace be upon him) commanded them, when traveling, not to remove their khuffayn for three days and nights, except for janabah, but rather for excretions, urine, or sleep (which cause minor impurity).