User blog comment:ArtismScrub/Hierarchical Cardinal Notation (HCN)/@comment-80.98.179.160-20180227124011/@comment-30754445-20180227203826

But if you're using Ordinal Collapse, what's the point of having a Veblen analogue in the first place? OCF alone can do anything that OCF+Veblen can do.

Anyway, your Φ's seem to be very similar to Deedlit's χ function: Φα seems to fill a role similar to Deedlit's χ(α,*). The actual strength of the notation, of-course, can't be determined until you define the collapsing mechanisms in a precise way.