What is the ruling on a marriage that takes place without a guardian (wali), where the judge marries the man and woman in the presence of only two witnesses?

The majority of scholars consider marriage without a guardian (wali) invalid, meaning a woman cannot marry herself. However, Imam Abu Hanifa permits a free, mature woman to marry herself. If a Sharia judge marries a woman without a guardian, following the school of thought of Abu Hanifa, the marriage is valid.