User:12AbBa/Pi notation analysis

Pi notation is a strong ordinal notation invented by Username5243. It posses some curious properties:

\(f_\alpha(n) \approx g_{\pi(\alpha)}(n)\). Pi notation provides analysis between FGH ​​​​​​​and ​​​​​​​SGH.

Thus, it is also related to ​​​​​​​​​​​​​​Catching Function. In fact: