In section IIIA (p11) Max Tegmark tries to prove that the integrated information Φ of a bell state is zero. The definition of Φ that Tegmark uses is given by the mutual information I minimized over all possible factorizations. The bell state has I=2 when written in the usual basis. Tegmark then appears to argue that we can move to a basis in which the entire bell state is given by a single basis vector (and not a superposition of basis vectors), which is a completely factorizable state (which he apparently proves in equation 10) yielding Φ=0. What I don't understand is how that counts as a factorization? Surely the valid bases are the infinity of spin-space bases, none of which allow for Φ to be zero. Or am I confusing factorizations with bases somehow? Would love to hear from someone with a better grasp of the mathematical details!