Is the guardian a condition for the validity of the marriage contract, and does his absence invalidate the marriage?

The presence of a guardian (wali) is a pillar for the validity of a woman's marriage according to the majority of scholars, due to the Prophet's (peace be upon him) saying: "Any woman who marries without the permission of her guardians, her marriage is invalid." As for an adult, sane, and mature man, a guardian is not a condition for the validity of his marriage. However, if he is foolish, insane, or a minor, then the guardian's consent is necessary.