Negative tests with analytic reasons

Unauthorized recovery. For two-qubit access, the channel is constant and its best logical half-diamond error is $3/4$.

Uncounted workspace. A module's local peak must be added to the unaffected frontier. Counting only its returned output omits its live input or ancilla.

Premature destructive readout. Measuring $Z_1$ before applying the batch decoder removes the logical $Z$ and $Y$ components because their representatives anticommute with $Z_1$. Logical $X$ survives. The induced logical channel is $X$-dephasing, not recovery.

Readout substituted for quantum recovery. The programme of Proposition prop:observable correctly realizes a logical measurement instrument. Its unreported logical output is dephased and fails the identity task on a Bell input.

Hidden postselection. Keeping one syndrome branch retains probability $1/4$. Its selective logical map is $\rho \mapsto \rho /4$, not a trace-preserving decoder. Renormalization does not make it deterministic.

Off-code rank used as an intrinsic obstruction. Example ex:offcode gives correct restricted decoders with different Choi ranks. Only the faithful-syndrome uniqueness theorem justifies an intrinsic rank claim in our benchmark.