User blog comment:Hyp cos/Attempt of OCF up to Stability/@comment-35470197-20181026043805/@comment-35470197-20181027095023

> The definitions of the OCFs here are much shorter than the ones in the literature, which are several pages long.

It is irrelevant to notations. Could you answer my questions above?
 * 1) Do you have an ordinal notation system associated to your OCF?
 * 2) What does "notation" mean in your sense?

If you needed a simple OCF which does not have an associated ordinal notation system or does not have strength of an ordinal notation system, then you could define the simplest OCF \(\varphi(\mathbb{X},\alpha,\mathbb{Y},\beta) := 0\). But you are trying to more useful one, aren't you? Or do you need an OCF which is not useful for analysis or does not generate a large number?