User blog comment:Pellucidar12/Proof length function/@comment-1605058-20161226131313/@comment-30754445-20161228235733

Doesn't the exact length of a given proof depends on the implementation?

Sure this doesn't change the general growth-rate of the function, but it does change the specific resulting numbers. So unless we define, exactly, what we mean by "proof of length n", we don't have a well-defined function.

Also, if I remember correctly, Emlightened gave some reasons for the second type of function (the uncomputable one) to be not well-defined. Her argument also applied to Rayo's function. Didn't really understand it, but this may be relevant here as well.