User blog comment:Hyp cos/SCG(n) and some related/@comment-10429372-20140816062949/@comment-11227630-20140816094639

I've tried that, but it just reaches $$f_{\varepsilon_2+\varepsilon_0^2}(n)$$ for "large" n (say, larger than a googol but smaller than f_{e(2)+e(0)^2}(googol)).

The levels up to e(2) are the same, then the double edge links to two binary trees, up to e(2)+e(0)^2, finally the level e(2)+e(0)^2 graph is .edge.double edge.edge.loop