User blog comment:Ubersketch/Lexicographic ordinal notation up to the Bachmann-Howard ordinal/@comment-30869823-20190913225449

Your OCF doens't get to the BHO but only to \( \psi(\Omega\omega) \) since you can't express ordinals past \( \Omega\omega \) using only \( \Omega \) and addtion.

To fix it you could add \( \Omega \cdot \gamma, \Omega^\gamma \) to \( C_{n+1} \)