User blog comment:Plain'N'Simple/Letter Notation Up to Z: Outline and mnemonics/@comment-36984051-20191106024302/@comment-35470197-20191106095623

According to several googologists' guess without any theoretic background, (0,0,0)(1,1,1)(2,2,2) is considered to be well-founded and to correspond to an ordinal which is not expressed by UNOCF under the assumption that it were ill-defined, and UNOCF is stronger than any known OCFs under the same assumption. Therefore they would perhaps guess that (0,0,0)(1,1,1)(2,2,2) corresponds to X8 or a greater scale.

Also, Taranovsky considers TON or its variant as a conjectural candidate of an ordinal notation of PTO(Z_2+PD)-level. Therefore they would perhaps guess that TON corresponds to Z2 or Z3 scale.

To clarify, I would like to say thay I am not guessing the results. I have no idea on the termination of BMS or TON.