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This was a fun read! Two quick comments about Chapter 11. First, there is a "Euclidian" which should be a "Euclidean."
Second, I have a mild technical objection to your description of Equestria-space as not being commutative. "Noncommutative geometry" has a mathematical meaning (it is not completely precise yet because the field is relatively young), and it refers to something different, namely coordinates not being commutative (e.g. position and momentum in quantum mechanics). What you're describing is more like a Cayley graph of a noncommutative group. The bare graph itself has no notion of commutativity or noncommutativity: it's the extra fact that there are six specific ways to go from a block to one of its neighbors that look like elements of Z^3 for familiarity but that are actually elements of the free group on 6 generators or some quotient thereof.
I've fixed the spelling error.
If you could suggest a phrasing that's both accurate, but also short and won't require the reader to know much graph theory. I think I'm pushing it as it is right now. I said "noncommutative" since I assumed that basically my entire audience would have been exposed to commutative binary function from their high school proofs classes.
"Noncommutative" should be applied to the operations (up, left, etc.) rather than to the space. Where are you that it's typical for there to be classes on proofs in high school?
I went to high school in the United States and had a semester in proofs during high school. But now that you mention it, this may not be common and I might be generalizing from non-representative schools...
My understanding of what's typical in American high schools is that most students only get as far as trigonometry or precalculus. Stronger students will take some form of calculus. But even at that point the closest thing a typical student will come to taking a course on proofs is seeing some "two-column proofs" of statements in Euclidean geometry.
That seems accurate to me.