User blog comment:Maxywaxy/Do any functions reach this growth rate?/@comment-37246647-20181207032436/@comment-11227630-20181207093458

I conjectured that strong array notation has a growth rate of "the supremum of computable collapsing of \(\alpha\) that is \(\omega^\text{CK}_{\alpha+n}\)-stable for all n" in FGH. In another word, for all natural number n, it may eventually surpass all provable recursive functions in KP + "there exists \(\alpha\) that is \(\omega^\text{CK}_{\alpha+n}\)-stable".

Some OCFs by Micheal Rathjen go beyond that, and so does Taranovsky's ordinal notation.