An exact non-Clifford responding program

This is the properly completed “responding non-Clifford” fragment: a specified non-Clifford coupling and a direct residual witness, rather than an inference from gate classification alone. The baseline $\theta =0$ is nonresponding, and the response is proved on the same code, preparation, and partition.

For small $\theta$,

The exact relation is

This relation belongs to this family, not to arbitrary encodings.

Magic on $|{\Psi }_{\theta }⟩$ vanishes at both endpoints, while leakage is zero only at the first endpoint. Thus even in this entangling family, leakage is not a faithful magic measure.