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This is FGH of the notation of this game:

http://googology.wikia.com/wiki/User_blog:Alejandro_Magno/Make_an_extension_of_the_Notation!_(my_style)

It's called Hyperion Notation.

Things from 0#n to (0)#n is Basic Hyperion Notation

Things from (0)#n to ((0))#n is Brace Hyperion Notation

Things from ((0))#n to (0,1)#n is Extended Brace Hyperion Notation

Things from (0,1)#n to (0[1]1)#n is Linear Brace Hyperion Notation

Things from (0[1]1)#n to (0[2]1)#n is Planar Brace Hyperion Notation

Things from (0[2]1)#n to (0[0,1]1)#n is Multi-Dimensional Brace Hyperion Notation

Things from (0[0,1]1)#n to (0,11)#n is Nested Dimensional Brace Hyperion Notation, or Super-Dimensional Brace Hyperion Notation

Things from (0,11)#n to (0,0,11)#n is Multi-Level Separator Brace Hyperion Notation / Double-Dimensional Brace Hyperion Notation

Things from (0,0,11)#n to (0[0][0][1]1)#n is Nested Level Separator Brace Hyperion Notation

Things from (0[0][0][1]1)#n to (0[0],[1]1)#n is Multiple-Dimensional Brace Hyperion Notation

Things from (0[0],[1]1)#n to (0[0]0,1[1]1)#n is Array-Dimensional Brace Hyperion Notation

  1. Things from (0[0],[1]1)#n to (0[0][ [1] ][1]1)#n is Linear Array-Dimensional Brace Hyperion Notation
  2. Things from (0[0][ [1] ][1]1)#n to (0[0][ [0] ][ [1] ][1]1)#n is Multi-dimensional Array-Dimensional Brace Hyperion Notation
  3. Things from (0[0][ [0] ][ [1] ][1]1)#n to (0[0][ [0] ],[ [1] ][1]1)#n is Multiple-dimensional Array-Dimensional Brace Hyperion Notation

Basic Hyperion Notation

0#n has level f_1(n)

1#n has level f_2(n)

2#n has level f_3(n)

m#n has level f_1+m(n)

(0)#n has level f_w(n)

Brace Hyperion Notation

(0)#n has level f_w(n)

(0)1#n has level f_1(n)

(0)m#n has level f_m(n)

(0)(0)#n has level f_w*2(n)

(0)(0)(0)#n has level f_w*3(n)

(1)#n has level f_w^2(n)

(1)(1)#n has level f_w^2*2(n)

(2)#n has level f_w^3(n)

(m)#n has level f_w^(1+m)(n)

((0))#n has level f_w^w(n)

Extended Brace Hyperion Notation

((0))#n has level f_1+w^w(n)

((0)1)#n has level f_w^(w+1)(n)

((0)m)#n has level f_w^(w+m)(n)

((0)(0))#n has level f_w^(w*2)(n)

((1))#n has level f_w^(w^2)(n)

((1)(1))#n has level f_w^(w^2*2)(n)

((2))#n has level f_w^(w^3)(n)

((m))#n has level f_w^(w^(1+m))(n)

(((1)))#n has level f_w^w^w(n)

((((1))))#n has level f_w^w^w^w(n)

(0,1)#n has level f_e(0)(n)

Linear Brace Hyperion Notation

Aarex calculated:

(0,2)#n has level fe1(n)

(0,3)#n has level fe2(n)

(0,(0))#n has level few(n)

(0,(0,1))#n has level fee0(n)

(0,(0,(0,1)))#n has level feee0(n)

(0,0,1)#n has level fz0(n)

(0,1,1)#n has level fez0+1(n)

(0,(0,0,1),1)#n has level fez0*2(n)

(0,0,2)#n has level fz1(n)

(0,0,0,1)#n has level feta0(n)

(0[1]1)#n has level fphi(w,0)(n)

Planar Brace Hyperion Notation

Aarex calculated:

(0,1[1]1)#n has level fphi(w,0)*e0(n)

(0[1]2)#n has level fphi(w,0)w(n)

(0[1](0))#n has level fphi(w,0)w2(n)

(0[1]0,1)#n has level fphi(w,0)e0(n)

(0[1]0[1]1)#n has level fphi(w,0)phi(w,0)(n)

(1[1]1)#n has level fphi(w,0)*w(n)

(0,1[1]1)#n has level fphi(w,0)*e0(n)

(0[1]2)#n has level fphi(w,0)^2(n)

(0[1](0))#n has level fphi(w,0)^w(n)

(0[1]0[1]1)#n has level fphi(w,0)^phi(w,0)(n)

(0[1]1[1]1)#n has level fphi(w,0)^(phi(w,0)+1)(n)

(0[1]0[1]2)#n has level fphi(w,0)^(phi(w,0)*2)(n)

(0[1]0[1]0[1]1)#n has level fphi(w,0)^phi(w,0)^2(n)

(0[1]0[1]0[1]0[1]1)#n has level fphi(w,0)^phi(w,0)^3(n)

(0[2]1)#n has level fphi(w,0)^phi(w,0)^w(n)

(0[3]1)#n has level fphi(w,0)^phi(w,0)^w^2(n)

(0[(0)]1)#n has level fphi(w,0)^phi(w,0)^w^w(n)

(0[(0[1]1)]1)#n has level fphi(w,0)^phi(w,0)^phi(w,0)(n)

(0[0,1]1)#n has level fephi(w,0)+1(n)

Multi-Dimensional Brace Hyperion Notation

Aarex calculated:

(0[0,1]1)#n has level fephi(w,0)+1(n)

(0[0,2]1)#n has level fephi(w,0)+2(n)

(0[0,0,1]1)#n has level fzphi(w,0)+1(n)

(0[0[1]1]1)#n has level fphi(w,1)(n)

(0[0[0[1]1]1]1)#n has level fphi(w,2)(n)

(0,11)#n has level fphi(w,w)(n)

Nested Dimensional Brace Hyperion Notation / Super-Dimensional Brace Hyperion Notation

Aarex calculated:

(0,11)#n has level fphi(w,w)(n) Feel free to continue analysis.

Multi-Level Separator Brace Hyperion Notation

Feel free to do analysis.

Nested Level Separator Brace Hyperion Notation / Double-Dimensional Brace Hyperion Notation

Feel free to do analysis.

Multiple-Dimensional Brace Hyperion Notation

Feel free to do analysis.

Array-Dimensional Brace Hyperion Notation

Linear Array-Dimensional Brace Hyperion Notation

Feel free to do analysis.

Multi-dimensional Array-Dimensional Brace Hyperion Notation

Feel free to do analysis.

Multiple-dimensional Array-Dimensional Brace Hyperion Notation

Feel free to do analysis.

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