Khang2009's Massive Number

This is a massive number, written as $$\kappa^{2009}_{1}$$

Definition
I define a function:


 * $$\kappa_1 = 10^{100}$$
 * $$\kappa_{n+1} = f_\alpha(\kappa_n)$$ where $$\alpha$$is a largest limit ordinal satisfies $$g_{\alpha}(3) = \kappa_{n}$$ (using FGH and SGH)
 * $$\kappa^{m+1}_n = \kappa_{\kappa^{m}_n}$$
 * $$\kappa^1_n = \kappa_n$$

Khang2009's Massive Number ($$\kappa^{2009}_{1}$$)