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Ruby, 322 bytes, fψ9(9)(9)
where f is the fast growing hierarchy and ψ is an ordinal collapsing function described below.
def f(b,n=0)n<1?b.class!=Array:(n.times{n+=b==1?n:f(g(n,b),n)};n)end;def g(n,r)a,b=r;f(r)?(r>1?r-1:n):r.size>2?h(n,a,b):b>1?[a,b-1]:b>0?a:[a,n]end;def h(n,a,b)(x=b!=0?[a,i(n...
