Remark: Selective spectator states

For an entangled pair $(|00⟩+|11⟩)/\sqrt{2}$, local projective readout leaves the remote marginal $I/2$ nonselectively, but its conditional states are $|0⟩⟨0|$ and $|1⟩⟨1|$. Thus (iv) is not a claim that the spectator state is unchanged on each outcome. Nor may a subsequent controller inspect an otherwise excluded spectator record without changing the hypothesis.