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If you look at it carefully, Kairi has many things that are not becoming of a Princess:
One, she is thoroughly unapologetic about both kicking and stealing blankets in her sleep.
"Since when have I ever been able to win in tug-of-war against either of you?" she asks reasonably, and then ignores any protests that follow.
Two, she will sometimes steal the best pieces of candy out of a mixed bag before she shares.
"I paid for it with my money," she says. "Besides, I didn't take all of them -- if I just opened it around you two, I'd never get any."
Three, when she is convinced she is right, there is nothing that will change her mind.
"You're not any darker than I am," she will tell him when she puts both her hands on his face -- and he can't help but think that they were soft, years ago, but there are growing calluses on her fingertips and palm from the grip of a Keyblade. "You aren't, and if you keep saying that, I will hit you. Hard!"
... Corollary to three is that: because of her unshaking conviction that She Is Right, she tends to trust people who are very bad for her, and ultimately should have just been left alone.
"I really WILL hit you, so stop it!" --not that she does, but she glares very threateningly and maybe steps on his foot a little instead.
Four, when she IS right, which is not saying that she always is, she's usually very smug, because she doesn't actually participate in any of their small competitions, but she's the Winner, and she's not afraid to let anyone know it.
"Tonight," she says, framed by the setting sun, "let's go to the island together and stay until dawn. That's your punishment, you have to do what I say."
Five, if you see her reflection in the water or a window late at night -- never a mirror, they reveal too much -- you can see there's a shadow behind her reflection with wheat-blonde hair and ghostly pale skin. But Kairi claims to never see anything if this gets pointed it out to her.
"I want to think she's at rest," she says and puts both her hands over her heart without looking directly at either of them. "I want to believe that she's sharing my heart and she's happy with that. The things she had to do were so horrible, I don't want to think of her suffering any more."
Six, if you nudge her just so, she gets angry very easily.
"She deserved it," she mutters, as he and Sora drag her away from the surprised girl who's crying and holding her slapped cheek. "Saying all those horrible things about you two, when she doesn't even know what you guys have done."
And number last -- and she argues this a lot -- she is entirely too practical.
Because the other Princesses had spent most of their time captured staring out windows and waiting silently, patiently, for heroes that never came, but Kairi reasons aloud that if Sora is half an hour late to the meeting spot then obviously he is still asleep, and they should go to his home right away and teach him a lesson, probably involving pillows or a cup of ice water.
"If you try to leave me behind again," she warns, "I'll come after you, and then you'd better watch out." And usually at this point she is sitting on one or the other and she frowns until they both nod at her.
And Riku thinks that even though there are a thousand and one more ways that Kairi perhaps doesn't fit the original description of a Princess, it must be fine. Someone who is entirely pure and without darkness could never even touch someone who walks the twilight, for fear of being soiled.
But Kairi takes his head in both hands and she very carefully knocks their foreheads together -- not like with Sora, who will headbutt and call it a greeting -- and she smells not of perfume or flowers or expensive things like all the other Princesses that Riku has ever met, but of soap and the ocean and warm skin, and so Riku barely hesitates before he puts his arms around her waist and holds her loosely, blinking up at her.
"I won't be the one left waiting," she says. "Next time, I'm coming too."