User blog comment:Hyp cos/SCG(n) and some related/@comment-10429372-20140812170828/@comment-1605058-20140812190327

I'm still not convinced. It is possible, though unlikely, that discrepancy between (okay, fine, no 's) FSes given by graphs and standard ones is so huge, that e_2 graph actually leads to growth rate of (say) f_e_1. I don't think it's hard to see that f_e_2(10^10^21100) is considerably larger than f_e_1(2^^^^^5).

Note: I'm not saying that there is no way to justify your actual bound, I'm just saying that full proof would be quite hard. But that's how googology is - 10% formality, 20% estimates, 20% guessing, 50% handwaving.