User blog comment:Denis Maksudov/Fundamental sequences for extended Veblen-function/@comment-5529393-20170225185518

You should probably include $$\alpha_{m,i} > 0$$ in your list of rules for normal form. Otherwise people won't know that $$\varphi(z,\gamma) =  \varphi(\gamma)$$, so that you should use the single-variable rules in such cases. Other than that, looks good!