I say, and with God's success: There are conditions for the permissibility of wiping over the socks: First: the conditions for wiping over the khuffayn (leather socks). Second: they must be either soled or thick if they are not soled or leathered: the soled is one that has leather on its bottom, like the sole of the foot in the apparent narration. The leathered is one that has leather on its top and bottom, and this condition exists because the soled or leathered can withstand walking on them, and the concession is for this reason, thus it became like the khuff. The thickness requirement, if they are not soled or leathered: 1. They must not be thin and transparent such that what is underneath them can be seen by the observer and they do not conceal what is behind them. 2. Water must not pass through them. 3. They must stay on the leg without tying. The permissibility of wiping over the socks is inferred from the previous conditions: from the hadiths permitting wiping over the khuffayn, along with the hadith of Al-Mughirah ibn Shu'bah : "Indeed, the Messenger of Allah  performed ablution and wiped over the socks and the sandals," in Sahih Ibn Khuzaymah 1: 99, Sahih Ibn Hibban 4: 167, Jami' at-Tirmidhi 1: 167, which he authenticated, Sunan Abu Dawood 1: 41, Sunan an-Nasa'i al-Kubra 1: 92, and Sunan Ibn Majah 1: 185. However, the general permissibility of wiping over the socks is not acted upon based on this hadith. The scholar and hadith expert Al-Banuri said in Ma'arif as-Sunan 1: 350-351: "In summary, they did not act upon the generality of the hadith, but it seems they acted by refining the criteria for the khuff, thus including what we mentioned, and in any case, if the hadith of the socks is authentic, it cannot be acted upon in its generality that includes both thick and thin; due to the opposition of the recited Qur'an. Yes, they acted upon part of it, either by adhering to it or by refining the khuff mentioned in the mutawatir narrations... Also, the hadith is narrated from Al-Mughirah through about sixty chains, and the wording of the hadith in question is mentioned only in this chain, so how can one be assured of it? Furthermore, the practice of some lenient people to wipe over thin socks has no basis in the Shari'ah to rely upon; if it is based on this hadith, you have known what is in it and what the imams said, and if it is based on the words of the jurists, they stipulated either leathering or soling, or at least thickness, and Allah knows best." The scholar Dr. Nur ad-Din 'Itr said in I'lam al-Anam Sharh Bulugh al-Maram 1: 187-188: "Some scholars relied on this hadith and permitted wiping over the socks regardless of their condition, and if you contemplate the hadith, you will find it narrating an actual incident, without clarifying the details of the type of sock that the Prophet صلى الله عليه وسلم wiped over, what its thickness was? Its durability? It may have been over the khuff or it may have had a sole, or it may not have been so, and it is well-known in the principles of jurisprudence that inferring from actual incidents requires knowledge of their circumstances and contexts. The truth is that it is not correct to use this hadith as evidence for what they have claimed, and it is indeed negligence and leniency regarding the Shari'ah. It has become clear that wiping over the khuffayn has been established by the mutawatir Sunnah and by the consensus on its permissibility... and that it is not correct to use... as evidence for the permissibility of wiping over the socks in an unrestricted manner. The Malikis and Shafi'is have prohibited wiping over the socks based on the apparent meaning of the verse on ablution, which is also the view of Imam Abu Hanifah, and they did not act upon this hadith of Al-Mughirah رضي الله عنه regarding wiping over the socks, and their excuse for that has become clear. However, we see the possibility of acting upon the hadith if we relate it back to the original issue — which is wiping over the khuffayn — if the sock meets the characteristics of the khuff, we permit wiping over it, otherwise it is not permissible, and this is the position of Imam Ahmad and the companions of Abu Hanifah, Abu Yusuf and Muhammad, and this is the fatwa in the Hanafi school, and we say: it is permissible to wipe over the socks if they have this description: that they are thick, meaning they are substantial, and that one can walk in them... And there is also an agreed-upon condition that the sock must stay on the foot by itself without tying, and based on this, what meets those conditions of socks is valid for wiping over, and what does not meet them is not permissible to wipe over according to the agreement of the diligent imams." And see: Radd al-Muhtar 1: 179, Al-Ithaf Q7/B, Al-Taybin 1: 52, Nihayat al-Mirad p. 389, Al-Hadiyyah al-Alaiyyah p. 39, and Bada'i' al-Sana'i' 1: 10, and Allah knows best.