User blog comment:Googleaarex/SGH Functions/@comment-25418284-20130404163840

SGH has the interesting effect of replacing \(\omega\)s with \(n\)s. (That's why it makes an appearance in BEAF, because we need to replace \(X\)s with \(p\)s.)

If I have it correctly...

\(g_{\varepsilon_0}(n) = n\uparrow\uparrow n\) because \(\varepsilon_0 = \omega \uparrow\uparrow \omega\).

\(g_{\varphi_m(0)}(n) = n\uparrow^{m + 1} n\)?

That's how I get \(g_{\Gamma_0}(n) \approx n\ \{\{1\}\}\ n\), but Deedlit has told me this is wrong :/