5
Python 2, 197 bytes, ~ Hψ(ΩΩΩ)(9)
where H is the Hardy hierarchy, and ψ is the ordinal collapsing function below the Bachmann-Howard ordinal defined by Pohlers.
def S(T):return 0if T==1else[S(T[0])]+T[1:]
def R(T):
U=T[0];V=T[1:];global B
if T[-1]==0:B=T
if U==1:return[S(B)]+V
return[R(U)]...
