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

If level-$$\alpha$$ turing machines has growth rate of $$\omega^{CK}_{\alpha}$$, then Nishada's Ordinal would be equal to $$\psi(\Omega^{\omega})$$ where $$\psi$$ is tweaked with changed rule: $$\psi(n) = \omega^{CK}_n$$

And yeah, these turing machines are possible because of oracles.