User blog comment:Fluoroantimonic Acid/(C) FGH up to phi(w,0)/@comment-5529393-20150812175134/@comment-5529393-20150813020931

One of your calls to _fast_growing_hierarchy has four variables rather than three.

As far as how to represent ordinals, ord = {ord, int, int} doesn't seem to be enough to get to phi(w,0). The natural representation for ordinals up to Gamma_0 is of the form

$$o = \varphi(\alpha_1, \beta_1) + \varphi(\alpha_2, \beta_2) + \ldots + \varphi(\alpha_n, \beta_n)$$

so the natural data structure to represent this is a pointer to an array, like in your Kirby-Paris hydra program, but rather than each array element pointing to an ordinal, each array element should be a pair of ordinals (alpha_i and beta_i).