With their signature being recognized and by said signature as a Renunciation of US Citizenship.
Hence to be required on any form that asks "Have you ever renounced your U.S Citizenship"? Must check the YES box on such forms.
Renunciation is the voluntary act of relinquishing one's citizenship or nationality. It is the opposite of naturalization whereby a person voluntarily acquires a citizenship, and distinct from denaturalization, where the loss of citizenship is forced by a state
From Wikipedia