Inside Alex's Dantian, the Yang source and the Yin bead remained in eternal harmony. The Yin bead appeared stronger than the Yang source to Alex's senses, but that was only because it gave off more Yin than the Yang source gave off Yang.
In a way, the Yang source contained itself far better than the Yin bead did.
If the two were in any other person's dantian currently, they would no doubt be at an imbalance, causing the person's Qi to run cold with Yin. However, because it was Alex, his Qi itself was fully Yang from the start because of his Sun God's Celestial Yang body, which counteracted the Yin bead.
In a way, it wasn't the Yang source and Yin bead that were in strife, but rather his body and the Yin bead. And his body lost because the Yin bead was stronger.
It was the addition of the Yang source that balanced the Yin and Yang.
