User blog comment:Pellucidar12/Attempt at a FGH related notation/@comment-28606698-20170415185346/@comment-1605058-20170416115327

I don't know where you see a problem here. This notation isn't a kind that resolves into itself - instead, you take the inputs and plug them into FGH in a prescribed way. As long as you have FGH worked out (and this only needs fundamental sequences to be specified), no problems arise. There is no need to have a bridge anywhere and jumping from small computable ordinals to admissible ordinals is perfectly fine.