User blog comment:Googleaarex/A new, really strong OCF definition?/@comment-28606698-20170801202840/@comment-28606698-20170801210145

Yes, I agree. But how to assign FS for this case?

here and here we can see two rules for case if argument is a limit ordinal depending on its cofinality. I see you tried to do something in this kind but unfortunately I still did not understand your $$\psi(\beta[\alpha])$$

By the way seems in section rules couple of bugs:

In rule 2 should be $$D[0]$$ in right part

In rule 5 should be $$\beta$$ in right part