User blog comment:Deedlit11/Ordinal Notations VI: Up to a weakly compact cardinal/@comment-5150073-20140515153351/@comment-10429372-20140521151454

Yes, although I prefer lim(n->w)f^n(0). There is only a small problem, there is no innermost value, so although it is the good value, it will be considered ugly by most ordinal collapsing function experts.