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Based on psychology, he was sure she was Mafia, based on her status, she was aggressive. Of the aggressive roles, only Knight and Fragment remained. On the third night, there was no visible Mafia kill for the second night; Nebula was blocked, which means he was the father (then the Master) or a monster. Later, I was explained that Nebula was definitely not the father. Why isn't Lynx the father? Because there's no kill from the father on the second night, and no one blocked her. This leaves the possibility of a liar, or that the father's turn was spent on Nefelu, but that would be an unproductive coincidence that can be ignored, like, for example, trying to account for untraceable and completely random non-deductive tabletop elements in interpreting the newspaper, or like linking the absence of kills on any night to being in natural protection.
Okay, so it turns out that the conclusions were correct.