SDP acceptance is not a status string

The SDP formulations are given in Appendix app:sdp. Every requested solve first archives raw variables, constraint duals, settings, and solver statistics, before residual checks or another solve. Failure therefore preserves any obtained decoder.

For complex PSD constraints, the implementation uses realification:

It separately checks Hermiticity of every relevant original matrix. CVXPY constraint residuals and solver statistics are recorded as diagnostics CVXPYConstraints,CVXPYAdvanced,CVXPYSolvers. Independent original-matrix residuals determine acceptance.

The declared floating-point tests are:

1. finite values and acceptable solver status;

2. Hermiticity residual and Frobenius norm of the negative spectral part at most $3\times 10^{-4}$;

3. affine residual Frobenius norm at most $3\times 10^{-4}$;

4. independent primal–dual objective difference at most $5\times 10^{-4}$;

5. Choi positivity and trace preservation for every encoded or decoded channel;

6. agreement with analytical controls at most $5\times 10^{-4}$.

Raw and repaired decoder residuals are both retained. A numerical decoder repair is not an interval certificate. Agreement of objectives is insufficient without feasibility.