User blog comment:Plain'N'Simple/Letter Notation Up to Z: Outline and mnemonics/@comment-36984051-20191106024302/@comment-35470197-20191106145802

> Unfortunately it's a useless upperbound, because nobody dares to attach an actual ordinal to (0,0,0)(1,1,1)(2,2,2).

Exactly. But the upperbound is helpful when people consider a direct extension of TSS. Although they do not have the termination of such a notation, but they are free from "weaker-than-UNOCF" crisis.

It would be good if there were an effective upperbound. However, it is impossible for OCF users to give an edivence because UNOCF is not comparable to any OCF by the lack of the formality. Therefore it relies on UNOCF users. If there would be a day in the future when a UNOCF user studies the greatest OCF (maybe the one for Stability by Stegert?), then he or she could tell us the answer.

> I would be interested to know the percentage of UNOCF users who'd concede that UNOCF is less powerful than (say) PTO(ZFC).

I guess that they agree with it as long as they have heard the word "PTO".

> I wonder how many UNOCF users believe that UNOCF is stronger than anything computable (which would, of-course, contradicts the notion that it is bound by (0,0,0)(1,1,1)(2,2,2), but they may not know that).

I have no idea. At least in Japan, BMS seems much more famous than UNOCF, and hence I guess that the majority of Japanese UNOCF users (I do not know whether there are many or not) doubt it. If BMS is globally much less famous than UNOCF, then such worship can occur.