What is the ruling on wiping over socks (khuffayn) according to the four imams, and what is its evidence, along with mentioning the names of the books?

The four madhhabs (schools of thought) agree on the permissibility of wiping over leather socks (khuffayn) due to the widespread and continuous transmission of its establishment from the Prophet (peace be upon him). As for wiping over regular socks (jawrabayn), it is generally permissible according to them, with differences in the conditions:

Hanafis: Wiping over socks is permissible without dispute if they are covered with leather (mujalladayn) or have soles (mun'alayn). As for those not covered with leather or without soles, it is permissible according to Abu Yusuf and Muhammad if they are thick and do not allow water to seep through, a view that Abu Hanifa himself adopted at the end of his life. Malikis: Wiping over socks is permissible on the condition that they are leather-covered on both their outer and inner surfaces. Shafi'is: They permitted wiping over them on the condition that they are thick (non-transparent) and that one can continuously walk in them. Al-Nawawi affirmed that having soles is not a condition. Hanbalis: Wiping over thick socks is permissible if they remain firm on the foot and one can continuously walk in them, whether they have soles or not.