No problem! I've been trying very hard to pare down my history sections to varying degrees of success, clearly.
1: Black Phantom is the organization that her father is the head of. It basically sells espers to the highest bidder for things like assassination, espionage, that sort of stuff. Yuuri was born with strong hypno so for as long as she's been able to she's been used as the brainwasher of the organization who finds espers who are strong and can be controlled and basically turn them into obedient "dolls".
2: Mirage is basically the part of Yuuri's personality that is cold, calm and obedient. Basically: Father's Good Girl who supports her father unquestioningly. On some subconscious level, Yuuri knew what she was doing for Father was wrong but also was brought up to think she had to listen to her father because he loves her and also she belongs to him and so she has to be obedient. Canon doesn't specify whether it's some sort of trauma caused Dissociative Identity Disorder or if it's just that her inability to reconcile her growing resentment of her father for forcing her to do these things combined with her being a high level esper caused this but the end result is that she had Mirage which is the Father's Good Girl personality, Phantom which was the rebellious, Fuck You Dad personality and then added to that was the Totally A Normal Girl fake personality of Yuuri that was created so she can do her undercover thing undetected. At her current canon point though, they're gone since she's resolved the 'people are free to make their own choices and so can I' issue in her life and the fake personality (which is hinted to be what she ideally would want to be) is now the basis of her real personality but with Phantom and Mirage's memories. If any of this didn't make sense, please let me know!
3: Hyoubu Kyousuke is the leader of PANDRA. The boy who escaped is a side character called Bullet.
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1: Black Phantom is the organization that her father is the head of. It basically sells espers to the highest bidder for things like assassination, espionage, that sort of stuff. Yuuri was born with strong hypno so for as long as she's been able to she's been used as the brainwasher of the organization who finds espers who are strong and can be controlled and basically turn them into obedient "dolls".
2: Mirage is basically the part of Yuuri's personality that is cold, calm and obedient. Basically: Father's Good Girl who supports her father unquestioningly. On some subconscious level, Yuuri knew what she was doing for Father was wrong but also was brought up to think she had to listen to her father because he loves her and also she belongs to him and so she has to be obedient. Canon doesn't specify whether it's some sort of trauma caused Dissociative Identity Disorder or if it's just that her inability to reconcile her growing resentment of her father for forcing her to do these things combined with her being a high level esper caused this but the end result is that she had Mirage which is the Father's Good Girl personality, Phantom which was the rebellious, Fuck You Dad personality and then added to that was the Totally A Normal Girl fake personality of Yuuri that was created so she can do her undercover thing undetected. At her current canon point though, they're gone since she's resolved the 'people are free to make their own choices and so can I' issue in her life and the fake personality (which is hinted to be what she ideally would want to be) is now the basis of her real personality but with Phantom and Mirage's memories. If any of this didn't make sense, please let me know!
3: Hyoubu Kyousuke is the leader of PANDRA. The boy who escaped is a side character called Bullet.