User blog comment:Edwin Shade/Rank-on-Rank Turing Ordinals and Beyond/@comment-5029411-20180119221837/@comment-80.98.179.160-20180120175857

Define $$\psi^\text{CK}(\alpha)$$ as exact same as the original Madore psi, but added functions: epsilon, zeta, Veblen, Weiermann theta, Rathjen psi, and Church-Kleene maps.

Then, $$\psi^\text{CK}(\zeta_0^\text{CK})=\zeta_0^\text{CK}$$, with the next ordinal where it's not constant is omega-one. It continues with omega-one squared->eta-0 CK, omega one to omega one->$$\Gamma_0^\text{CK}$$