Is a woman who abandons the hijab considered a fasiq (transgressor), even if she acknowledges its obligation, and what is the proof for that?

A woman who abandons the hijab while acknowledging its obligation is considered a transgressor (fasiqah) because she has departed from obedience to Allah. Transgression (fisq) is the departure from obedience to Allah into disobedience. If a woman displays her adornment (her natural adornment, such as revealing her face and neck, or acquired adornment, such as kohl and colored clothes) while believing that this is not permissible, she is a transgressor and must repent. However, if she believes that this is permissible, she is a disbeliever (kafirah), as she has contravened the Qur'an, which forbade her from displaying adornment to anyone other than those who were exempted.