User blog:Mh314159/Natural number recursion -- first 6 rule sets

In another blog post I was advised to study ordinals (to get over my fear, which really was not the issue) and I have done a little of that, watching some videos that go past epsilon and zeta and into the Veblen structure. I think I understood everything before Veblen pretty well, but only some of what came after, would need to spend more time on those. My original goal was to see how large a number I could define and I don't really want to do it by using pre-existing work. Anyway, it doesn't help me with my natural number recursions because I cannot find the clear conversions between the FGH and my recursions. I have a hard time understanding what the FS is for any given rule in my notation. Here are my rules up to rule 6, with much stronger rules planned beyond that.

(I am having trouble getting the formatting to copy over from my text document: will post as soon as I have solved that problem)