User blog comment:Ubersketch/Fundamental sequences for CK and higher?/@comment-35295276-20181025210550

I don't know much about ITTM's but for the Church-kleene ordinal i think the fundamental sequence is that the nth term is the largest ordinal expressible by an n-state turing machine.

This is why (\f_{\omega_1^{CK}(n)\approx BB(n)\)