User blog comment:Googleaarex/A new, really strong OCF definition?/@comment-5529393-20170730222010

You write $$\beta = \min \{ \beta | \beta < D_{\gamma+1} \}$$, but that's zero.

You have $$\psi_{D[0]}(0) = \alpha$$ such that $$\alpha = \omega^\alpha$$, but that is true of any epsilon number, so that is not a good definition. Did you perhaps mean $$\varepsilon_0$$?