User blog comment:QuasarBooster/Laver tables in Python/@comment-34422464-20181211142242/@comment-35470197-20181211223137

I see. Unprovability under ZFC and provability under ZFC plus I0 does not ensure the strength.

Also, if I0 is consistent, then q(n) is much smaller than the extended transcendental system to ZFC plus I0 by definition. So it is an example of a computable function greater than q(n). (It does not give a meaningful upper bound though, because such a transcendental system does not have a known effective upper bound.)