Round 2 verification audit for C012

Model: gpt-5

Claim: A pulse of duration t gives U_A = exp((alpha(t) a^dag - alpha*(t) a) S_{x,e}) exp(i Phi(t) S_{x,e}^2) with alpha(t) = -i (eta Omega/delta) e^{-i delta t/2} sin(delta t/2) and Phi(t) = (eta^2 Omega^2 / 4 delta^2)(delta t - sin(delta t)).

Source alignment: source/main.tex:116-119 (Eq. (2))

Prior official verdict: verified with failure_reason None.

Executable evidence: sympy_check.py. Sandbox rerun logs: sympy_check.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: Derive the MS propagator by Magnus expansion of H_A and confirm the displacement amplitude alpha(t) and geometric phase Phi(t) expressions.. 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: Magnus expansion truncates at 2nd order ([H(t1),H(t2)] is a c-number*S_xe^2) and factorizes. alpha(t)=-i(eta Omega/delta)e^{-i delta t/2}sin(delta t/2) matches EXACTLY (sympy). Phi(t)=(eta^2 Omega^2/4 delta^2)(delta t - sin delta t) matches in magnitude; Magnus gives -Phi, an overall sign convention from the sign of H_A (only |Phi| matters). Numerical time-ordered integration vs factorized U_A: max|dU|=2.3e-12. Verified.