User blog comment:Rgetar/Veblen-like collapsing function up to Buchholz ordinal/@comment-35470197-20181128093835/@comment-35470197-20181128215932

You just removed the descriotion of them? Then it is not well-defined again.

Moreover, since you just defined the notion of "standard form" only for additive principal ordinal (Cantor normal form term in your sense), the notion of the cofinality is not well-defined in your way. It heavily depends on an additional assumption on the injectivity of your OCF.