User blog comment:Hyp cos/SCG(n) and some related/@comment-10429372-20140812170828/@comment-5529393-20140812192859

I understand your point, LittlePeng9, it is true that Wythagoras has not rigorously demonstrated how SCG(1) will stack up against the Hardy hierarchy with a "standard" FS, and it is likely that a rigorous proof will be quite difficult. But to me, it is not a reasonable belief that F_e_2 using the graph FS has the same growth rate as F_e_1 using the standard FS; it is "intuitively clear" to me that the various offsets we get with the graph FS compared to the standard FS do not "add up", the offsets are quickly swamped by the enormous increasing growth rates of the functions. Yes, this is handwaving, but the intuition is quite strong here, and it's the best we're going to get very likely.

Anyway, it's the same thing we've been doing when evaluating TREE(n) or BHydra(n), etc., or when we assume FGH will not differ greatly with slight changes in FS.

I'm a little confused by your statement "f_e_2(10^10^21100) is considerably larger than f_e_1(2^^^^^5)", that seems to be opposite to what you were arguing.