The third one is based on the fact that Emperor Tenmu defeated Prince Otomo to ascend the throne and raised his own son Prince Kusakabe to the Crown Prince, so he made both wives of the Crown Princes report the change of crown prince to the Ise-jingu Shrine.
天武天皇が壬申の乱で大友皇子を破って即位し、自分の子の草壁皇子を皇太子としたことから、皇太子の交代をそれぞれの妃に伊勢神宮に報告させたという説。