Great work. Very descriptive and put me right in the heart of the action. Something you would find at a book store I would say. Well done.

Wow! This is a fine piece of work, a very easy read and hard to put down. With a few small changes I think it is publishable.
I have a few editing suggestions that I will send offline. Andy's review on Part 2 makes a good point about verbosity in some places. However it looks like you have done some work on the section called "The Equation." It seems very tight now and tells us something about the maturing Kalind and her labour to learn 'the art of balance.' (That is a novel concept ... rhythmic gymnastics as a martial art for self defence??? ;-)
I did wonder about the ending. Will you be posting other parts of your 'larger work in progress' so we can learn what happens? I can imagine Kalind becoming a despot like her uncle which would be very sad.
My only real complaint is that you set this story in a far future world, but except for the colony ruins there is nothing to make this sci-fi. It's maybe more accurately labelled fantasy or paranormal.
All the same ... so well done, a brilliant piece. Cheers!