Two systems with identical state-transition topology can have Phi greater than zero and Phi equal to zero, differing only by a permutation of internal binary labels, so IIT's Phi is not invariant under isomorphisms.
Consciousness as integrated information: a provisional manifesto
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Integrated Information Theory and Isomorphic Feed-Forward Philosophical Zombies
Two systems with identical state-transition topology can have Phi greater than zero and Phi equal to zero, differing only by a permutation of internal binary labels, so IIT's Phi is not invariant under isomorphisms.