I say, and with Allah's success: It is required in ablution to wipe a quarter of the head once: as He, Glorified and Exalted, said: {And wipe over your heads} Al-Ma'idah: 6, and the absolute command does not necessitate repetition; as narrated by Al-Mughirah  that the Prophet  said: "He performed ablution and wiped over his forelock - the forelock is one of the forelocks, and it is the hairline at the front of the head - and over the turban and over the leather socks," in Sahih Muslim 1: 231, Al-Mujtabi 1: 76, and Sharh Ma'ani Al-Athar 1: 31. And from Anas  in Sunan Abu Dawood 1: 36, and Sunan Ibn Majah 1: 187, and Musnad Abu Awanah 1: 218, and Al-Mustadrak 1: 275. This indicates that complete wiping is not intended. And because the "ب" (ba) in the verse indicates adhesion, and the action which is wiping has extended to the tool which is the hand; because when "ب" enters into the tool: the action extends to all that is wiped: like "I wiped the orphan's head with my hand," or to the place: the action extends to the tool, and the estimation is: and wipe your hands with your heads, which implies the complete wiping of the hand without the head, and its complete adhesion to the head does not usually cover more than a quarter, thus it is determined as intended from the verse, which is what is required. And if it is said: "I wiped the wall with my hand," it is intended to mean all of it; because the wall is a name for the whole, and it has been intended; because it is a place, and the place is what is intended by the transitive action, thus it is meant in its entirety. But if it is said: "I wiped with the wall," it is intended to mean part of it; because the original meaning of "ب" is that it enters upon the means, which are not intended, thus the complete wiping is not established, but what suffices from it is what is used to reach the intended goal, and if "ب" enters upon the place, the place is likened to the means, thus the complete wiping of the place is not established. And because it has become evident that a quarter is considered in many rulings: as in shaving a quarter of the head which makes the pilgrim lawful and does not make it lawful without it, and blood is required if he does it in his state of Ihram and is not required without it, and as in the exposure of a quarter of the private parts in the chapter of prayer that prevents the validity of the prayer, while less than that does not prevent, likewise here. Refer to: Sharh Al-Wiqayah p. 77-78, Badā'i Al-Sanā'i 1: 4, and Al-Bahr Al-Rā'iq, 1/15, and Allah knows best.