To aver is to declare something is true or to state. This verb has a serious tone, so you might aver something on a witness stand or you might aver that you won't back down to a challenge.
The verb aver comes to English via the Latin root words ad, meaning "to," and verus, meaning "true." The word can have the sense of formally declaring something is true, but it can also mean to report positively: "The grandmother averred that her granddaughter would make a fine veterinarian because of her love and caring for animals."