Sentence:  There are ... brought all the way from Bougainville to present their birth certificates and testify in this courtroom, under <WSD>oath</WSD>, as to their given names. 
Meaning of the word marked with <WSD> tags:  A solemn pledge or promise, appealing to a deity, a ruler, or another entity (not necessarily present) to attest to the truth of a statement or sincerity of one's desire to fulfill a contract or promise.