Primitive Cascading Hyper Notation (PCHN) is the 7th part of HN.

Rules

An expression is of the form H<n,A>, where n is the base and A is an array.

1. If there is no array, H<n> = n^n
2. If the array's first entry is 1, delete it.
3. If the array is a sequence array, decrease it by one, then nest the whole expression into the base n times.
4. If the array is a limit array, change the array into the nth member of it's FS.

Arrays

This part uses the same definitions as HBHN.

X+0 = X

X+A (A is sequence array) is the next sequence array after X+A-1.

X+A (A is limit array)'s nth member of the FS is X+FS(A,n).

Also, we will define a new function, FS(a,b), to make defining things easier. FS(A,b) is bth member of A's FS.

Thanks to Aarex for helping define [X+[X+A]] and [X+X+A] cases.

If we find X... (call that A)

First find the block (as N) that contains A.

Then

We define block layer

Define N0 = N

N1 = A block that contains N0

N2 = A block that contains N1

N3 = A block that contains N2

Repeat until

Nn = A array (not a block) that contains Nn-1

We need to define B that first Nx block that less than N0.

B is a shorthand for B(A)

And

B(N) = B but A replaces with N.

To compare two arrays A and B where A and/or B are of the form X+N (where N is array), the array which is of the form X+N will be bigger, but if both A and B are of the form X+N, compare the N of A with the N of B, and that is your result.