User blog comment:Simply Beautiful Art/The largest numbers ever written in a program./@comment-5529393-20171120171503/@comment-5529393-20171120230028

Okay, but by a diagonalizer for $$\psi_{M^M}$$ I mean an ordinal $$\gamma$$ such that $$\psi_{M^M}(\gamma + \alpha)$$ is the $$\alpha$$th fixed point of the function $$\beta \mapsto \psi_{M^M}(\beta)$$,  $$\psi_{M^M}(\gamma 2 + \alpha)$$ is the $$\alpha$$th fixed point of the function $$\beta \mapsto \psi_{M^M}(\gamma + \beta)$$,  $$\psi_{M^M}(\gamma^2 + \alpha)$$ is the $$\alpha$$th fixed point of the function $$\beta \mapsto \psi_{M^M}(\gamma \cdot \beta)$$, and so on. The fact that these processes exist for weakly inaccessible cardinals is a key part to the strength of the OCF, I believe. So I want to make sure that the same thing occurs in your function.