User blog comment:Eners49/The secret 0th hyper-operator?/@comment-35470197-20180726231426/@comment-35392788-20180727203911

The SGH can do anything the FGH can do, but it requires massive ordinals.

Then, it is true that the SGH eventually catches up to the FGH. Basically, g_a(n) is comparable to f_a(n) if there exists some k such that for all n, g_a(n+k) > f_a(n)

This first catching point is \(\psi(\Omega_\omega)\)

And then, up and down arrows do catch up. In general, weak n+1-ation (with down arrows) corresponds to n-ation (with up arrows). So they catch up at \(\omega\)