Independent certificate checklist

A submission or implementation archive should keep the following objects separate.

1. Encoding convention. The four generators, logical $X,Z$, normalized vectors (eq:encoding), and physical factor order are fixed. Changing a logical phase convention changes the required decoder correction and must be recorded.

2. Access certificate. The syndrome table proves all weight-one and weight-two compressions vanish. The stabilizer support table proves the relevant maximally mixed three-qubit reduction.

3. Batch certificate. The gates in (eq:U) conjugate the supported logical Pauli pair to the output Pauli pair. The common environment vector in (eq:factor) certifies coherence, not merely computational-basis probabilities.

4. Streaming certificate. Both classical record bits are priced. All four branch vectors have squared norm $1/4$ and preserve the same logical ray and its external reference. All branches are summed.

5. Lower-bound certificate. Faithful-syndrome uniqueness removes the off-code freedom. The negative partial-transpose eigenvalue is $-1/8$. The one-live-qubit interface forces a separable first-input Choi cut.

6. Tree certificate. Recovery identities are composed as channels with arbitrary spectators. Local module cost and schedule optimality are distinct from unrestricted recovery-channel optimality.

7. Distributed certificate. A message is a classical service of declared capacity. The four-message lower bound assumes the stated one-way model, not arbitrary distributed assistance.

8. Approximation certificate. Local implementation bounds refer to complete channels, including classical registers, in a compatible half-diamond metric. Selected-state numerical tests cannot replace those bounds.