User blog comment:Wythagoras/Catching function in normal ordinals/@comment-11227630-20140203095754/@comment-5150073-20140627111143

I didn't say about defining all FS's up to $$\omega_1^\text{CK}$$. And there won't be any catching points before we define it past $$\psi(\psi_I(0))$$, because there could be different ways to extend, giving different catching points.

Also, what about considering "weak catching function", which indicates catching points between HH and FGH? We know that they catch at every $$\epsilon$$, so as long as the sequence of $$\epsilon$$'s is defined, it is total.