User blog comment:Vel!/FGH Gripe/@comment-2033667-20150326185550/@comment-5982810-20150326231834

The problem with your example is that the conjectures we are arguing about are nothing like "TREE(3) > BB(10)". These results are not obtained without at least some heuristic evidence, as you suggest. For example, I came to the conclusion that E^ is on the order of e0 because the delimiter set is of this order-type, and because I understand that the primitive recursions that I'm stacking are equipotent with the stacking of successor cases in FGH. This was originally based on a pretty strong intuition the numbers. Now I can actually back that up with proof. I have already demonstrated it for two functions up to the "w" case. The only other source of destabilization would be the fundamental sequences, but mine are identical to those of FGH under the weiner hierarchy.

If you honestly think altering fundamental sequences makes such a big difference then guess what FUCK FGH. It's obviously FUCKING USELESS as a measuring rod then! Let's just invent our own standard, maybe the R-function, and then we can tell the professional mathematicians when they claim their "FGH" reaches beyond that DEFINE YOUR FUCKING FUNDAMENTAL SEQUENCES! OTHERWISE IT DOESN'T EVALUATE TO ANYTHING. There I just proved FGH doesn't exist.