User blog comment:Edwin Shade/Rank-on-Rank Turing Ordinals and Beyond/@comment-5029411-20180119221837/@comment-1605058-20180120101912

There is no evidence that level-\(\alpha\) have growth rate \(\omega_\alpha^{CK}\), see here. Additionally, transfinite-level Turing machines depend on certain choices in a similar way as FGH depends on fundamental sequences, and those choices have impact on how fast the busy beaver functions grow, see my reply to Edwin above.