What is incumbent upon a twelve-year-old girl regarding expiation for breaking an oath?

If the girl has not reached puberty, her oath is not valid to begin with. If she breaks it before reaching puberty, there is no expiation due upon her, by consensus, based on the Prophet’s (peace be upon him) saying: "The pen has been lifted from three: from the insane person whose mind is overcome until he recovers, from the sleeper until he awakens, and from the child until he reaches puberty." However, if she breaks it after reaching puberty, the majority opinion is that no expiation is required either, because her oath was not valid to begin with. But if she swears an oath after reaching puberty and then breaks it, then expiation for breaking an oath is due upon her.