Round 2 verification audit for C080

Model: gpt-5

Claim: The system evolves under the Lindblad master equation d rho/dt = -(i/hbar)[H_s,rho] + sum_j DL_j with DL_j = L_j rho L_j^dag - (1/2){L_j^dag L_j, rho}, and the singlet fidelity follows F(t) ~= 1 - C_0 e^{-R_t t}, R_t being the Liouvillian gap.

Source alignment: source/supp_content.tex:183-196 (Eqs. (S11-S13))

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: Confirm the master-equation form and that the long-time fidelity is governed by the Liouvillian spectral gap R_t.. 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: Lindblad/GKSL master equation + dissipator form confirmed (paper's Eq S12 'L_k' in anticommutator is a typo for L_j). qutip Liouvillian at (1.95J,2.58J,0.29pi,beta=J): exactly one zero eigenvalue (unique steady state), steady-state singlet fidelity = 1.000000, gap = 0.11424 J. mesolve from |dd> + tail fit 1-F=C0 exp(-Rt) gives R_fit=0.11424 J = gap exactly (ratio 1.0000). So F(t)~1-C0 e^{-R_t t} with R_t the Liouvillian gap is confirmed. Conclusion: verified.