Proposition: Independent coverage requirements

Two-probe equality of the stress family does not determine a multiplicity-register channel.

Proof. Append the same free scalar representation to the finite register in two completions. Use identity on the coefficient register in one completion and ${\mathrm{Ad}}_Z$ in the other, while keeping the scalar representation and both stress probes fixed. The scalar data agree exactly. The two qubit channels have half-diamond distance one, detected by a Bell input.