Does forgetting to wipe the head necessitate repeating the ablution, and what is the difference between the conditions for the validity of ablution and its pillars?

Wiping the head is a pillar of ablution, so whoever omits it, their ablution is invalid. If one remembers it soon after, they should repeat the wiping and wash their feet, observing the order. If one remembers it after a long time, they must repeat the ablution according to the Hanbalis, due to the obligation of sequential performance (muwalat). As for the conditions for the validity of ablution, they include: the cessation of that which necessitates it beforehand, intention, Islam, sanity, discernment, pure permissible water, removing anything that prevents water from reaching the skin, and performing istijmar (cleaning with stones or tissue) if there is impurity. Omitting a condition or a pillar, despite being able to perform it, affects the validity of the act of worship.