User blog comment:QuasarBooster/Laver tables in Python/@comment-34422464-20181211142242/@comment-35470197-20181212011825

Right. It is an open problem in mathematics, if I am correct.

Moreover, it is not known whether the totality is independent of ZFC or not. (Just no one has verified the totality under ZFC. It does not mean that it is not provable under ZFC.) If it is actually provable under ZFC, then it immediately obtains a new upper bound by the original transcendental integer system (under ZFC without assuming I0).