Update: Since the question was put on hold, work on this will continue on this notebook.
So long, and thanks for all the fish!
First, let me state that I am not a formally-trained mathematician, therefore please forgive my approximations and help me correct my errors. Second, I am looking for prior work related to what I would like to call Hypertype Theory. What follows is a short introduction to the topic. But before that, here are a few specific questions that will hopefully make this question less open-ended.
