User blog comment:P進大好きbot/New Googological Ruler/@comment-31580368-20190629142620/@comment-35470197-20190722140035

> It's still a huge gap. At the very least, it would be appropriate to spread the scale further apart at that point and leave the intermediate level as "To Be Determined".

I defined the ruler so that Therefore I did not mind the existence of the intermidiate levels of which no one seems to be working with large numbers. Well, I do not know many communities, and hence there might be many googologists who actually belong to the intermidiate levels. At least, I think that the ruler is sufficient in this community. Of course, rulers with less "gaps" are useful in other aspects, but there have already been such ideas by several other googologists, Therefore I decided to this kind of the ruler.
 * 1) it is suitable for a googologists to aim at the next level without skipping to study mathematical stuffs, and
 * 2) for each level N, there is expected to be a googologist of level N.

> The PTOs of various theories. And not having the fundamental sequences at hand (yet!) is not synonymous to complete ignorance.

Right. But don't you think that if googologists understand large numbers of levels below PTO(Z_2), then they will usually aim at transcendental integers before working on discovering fundamental sequences? At least, I do not know googologists who are actually aiming at PTO(Z_2), while I sometimes see several googosists try to understand transcendental integers. According to the purpose 1 above, I do not spread the scale for them.

> For any theory X, we can define f_PTO(X)(n) as follows:

Maybe many googologists tried the same thoughts (even if they do not know the definition of "proofs"). I have already argued on essentially the same formulation with Scorcher007 above.