Who has the right to determine when a child was born to a female slave relative to her manumission contract?

Primary text

If the mother claims she gave birth after her contract or after the master's ownership commenced, while the master claims it was before, the master’s word is taken upon his oath. This is the view of Al-Shafi'i. The basis for this is that the default state is that the female slave and her child are the property of the master, and the mother is claiming a status that prevents the master's established right to disposal.