Corollary: Scalar data do not determine agreement

No function of the copy-class structure, branch probabilities, and pairwise scalar visibilities alone decides whether ${\delta }_J(S)=0$. The states at $\theta =0$ and $\theta =\pi$ have exactly the same such data on the same interface, but discrepancies $1/2$ and zero.

Proof. The data equality and discrepancy inequality are Proposition prop:cancellation.