Round 2 verification audit for C040

Model: gpt-5

Claim: One cycle of the protocol is the superoperator S(Phi,gamma,theta) = S_C(theta) S_B(gamma) S_A(Phi), where S_A and S_C are the superoperator forms of U_A and U_C and S_B is the composition of two independent single-ion decay channels.

Source alignment: source/supp_content.tex:9-13 (Supp. Mat. S1)

Prior official verdict: verified with failure_reason None.

Executable evidence: run.py. Sandbox rerun logs: run.log.

Independent audit: I scanned the copied script for imports/shared helper dependencies and reran it through the sandbox. The code is self-contained in this attempt directory and targets the claim strategy: Construct each superoperator in vectorized (column-stacking) form and confirm the ordered product reproduces one full protocol cycle.. I checked the relevant family model rather than relying only on exit status; the rerun is treated as one reproducibility input.

Decision: Round 2 verdict is verified with failure_reason None and limitations []. Notes: Confirmed the column-stacking superoperator identities vec(U rho U^dag)=kron(U,U)vec(rho) (err 8e-17) and vec(sum_k K_k rho K_k^dag)=(sum_k kron(K_k,K_k))vec(rho) (err 0). S_B factorizes as two independent single-ion decay channels (err 1e-16). The ordered product S(Phi,gamma,theta)=S_C S_B S_A reproduces the by-hand physical cycle (apply U_A, then two-ion Kraus B, then U_C) to err <1e-16 at three parameter sets, while the reversed ordering disagrees (err ~0.3-0.5). Tolerance 1e-12; satisfied. Clean composition identity -> verified.