Why do we think Nyx has any connection to an Arbiter? I found the
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where the question of what the origins of Nyx's powers are was asked, and frankly what was said doesn't at all support the idea that she has any connection to an Arbiter. When asked if her powers came from an Apostle, an S rank monster or a weak monster, WeirdWorld simply confirms Nyx didn't get her powers from an Apostle, and beyond that to speculate on it ourselves. I can definitely see why some would latch onto that interpretation, considering how busted Nyx's powers are. But with Ella being able to identify what monster turned Nyx with the eyes she earned by completing a Rite, and the fact that it seems dual traits are a hard requirement for stuff like Soul, I heavily doubt it myself.
She probably does have some mixed lineage of Light and Darkness in her though. According to the speeches they give on the paths of god, they grant and end life respectively. But I'd guess she skews more towards Darkness, considering the anti-magic properties of her powers and having a natural connection to the Dream World with her little river Nyx of souls.