User blog comment:Edwin Shade/In Which I Try To Derive Values of Madore's OCF on My Own, and See How Far I Get/@comment-30754445-20171130210823

The fundmanetal sequence of ψ(Ω22+Ω3) is not what you've written.

You got the first step right:

ψ(Ω22+Ω3) = ψ(Ω22+Ω2+Ω)

But replacing the final omega with ψ(ψ(0)) is not correct, because you've already constructed ordinals bigger than ζ₀ = lim (0, ψ(0), ψ(ψ(0)), ψ(ψ(ψ(0))), ).

Try counting upwards from ψ(Ω22+Ω2) and see how high you can get before you need that 3rd Ω.

Hint: focus on ordinals of the form ψ(Ω22+Ω2+ψ(x)) and try to make x as large as possible while still following the rules.