User blog comment:Emlightened/Hypernomials (Γ₀)/@comment-5529393-20160120163011/@comment-27513631-20160121003708

The rightmost number is always an integer (or X, then immediately reduced to an integer), but I'm not seeing where the case XX comes into it. Although the left is fixed to an X (or integer), the right (and middle) of the operator are completely unrestricted, and could be any hypernomial of X. X<1>(X+1)=X^(X+1), as far as I can tell, would naturally occur early on when reducing (say) X<1>X<0>2.

The successor was done on lines 3 and 5 to make it collapse similarly to the Veblen hierarchy and avoid weakening at potential fixed points; the 4th line was a typo.