Circulation and the Fast-Growing Hierarchy

[Catullus]

It might be interesting to extend the hyper-operation hierarchy to transfinite ordinal ranks.

Yea, I believe that fast growing hierarchies are a tool that can be used to achieve this. If I recall correctly, I'd better check the literature, but someone important already tried to extend the lower hyperoperations to ordinals... was it by Doner and Tarski? I'll double check if needed... i have the paper somewhere.

Is it this paper An extended arithmetic of ordinal numbers?