I'm going to assume that this isn't a first chapter, but it's the first I've read, so take that into consideration when reading this critique.

This is a short scene and seems for the most part just to be filler from what happened before to what is going to happen next. There is no real significance to the scene. A lot of time is spent on the elevator, residents and guests and Airi's name. But are all of those things necessary for the plot?

Obviously, her name will. You've set the ground work for her family's history having a profound interest in her future. Most notably, the fact that people want her dead just because of her name. So, yes. Name is important.

But what about the elevator and her musings about the residents and tenants of the building? Is there a significance to the plot line or is that just added in to pass to the time in the elevator?

I ask because there is a large amount of this scene dedicated to it. If doesn't advance plot or character development, it's just a filler and pulls the reader away from the story.

I'm not sure what the mark is, but I find it very interesting. I'd rather hear more about that, than the elevator. If she has to fill her journey in the elevator with musings, then it should be something to keep the reader's interest. Give some back story on the mark, or more history on her family. There's a lull in the action, which is fine as long as you keep the interest there. Which off the wall musings don't do.

I love the cliffhanger ending. But that's only because I'm a glutton for punishment and I try to do the same in my own writing (well, at least when I'm writing something in chaptered form). Maybe a little more description at the end and a show of how the muscle gets her in the car. Something to amp up the action a bit?

Overall, I really liked this short snippet. The voice is wonderful and it's an easy read not bogged down by overly descriptive exposition or hard to grasp sentences.

Well done.