What is Asseveration?

Legal Definition
The proof which a man gives of the truth of what be says, by appealing to his conscience as a witness. It differs from an oath in this, that by the latter he appeals to God as a witness of the truth of what he says, and invokes him as the avenger of falsehood and perfidy, to punish him if he speak not the truth. Vide Affirmation; Oath; and Merl. Quest. de Droit, mot Serment.
-- Bouviers Law Dictionary
Legal Definition
An affirmation ; a positive assertion; a solemn declaration. This word is seldom, if ever, used for a declaration made under oath, but denotes a declaration accompanied with solemnity or an appeal to conscience.
-- Black's Law Dictionary
Legal Definition
The solemn affirmation of the truth of a statement.
-- Ballentine's Law Dictionary