Constructibility in Line Rider

Hey guys! I've been thinking about this for a while, and finally around to (trying to) write it neatly: constructibility in Line Rider. I'm talking about formal constructibility in geometry, as in, what can we construct using certain tools and rules. The classic example is compass-and-straightedge construction. Well, my question is: what is constructible using Line Rider? Because I wanted the answer to be "as much as compass-and-straightedge," I use some questionable rules, but I think it's all pretty reasonable (theoretically; in practice it's awful).

Here's the document: download link.

It's pretty badly written, especially since I've never really written about math in English, but hopefully for the 0 of you who are interested, you can understand roughly what I mean. And if you have any corrections or improvements (like weakening the axioms), please let me know!

By the way, the idea was to use as few rules as possible, so I wasn't going to use the special line-adjusting features of LRA and LRJS. I still had to use XYZ snap.

It's a bit contrived, but I see what you're getting at. It'd probably be more interesting if there was a version of line rider that actually represented points in terms of rational or algebraic numbers rather than floating point approximations, since otherwise this sort of thing doesn't really hold up.