Round 2 verification audit for C044

Model: gpt-5

Claim: With alternating drives theta_1=pi (odd) and theta_2=pi/2 (even), the two-cycle superoperator S(pi/4,gamma,theta_2)S(pi/4,gamma,theta_1) has only three non-zero eigenvalues: lambda_ss=+1 and lambda_pm = (1/4)(1 +/- 3 sqrt(1 - (2/9)[2+cos^4(gamma)] sin^2(2 gamma))).

Source alignment: source/supp_content.tex:43-46 (Eq. (S3))

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: Symbolically diagonalize the two-cycle alternating superoperator and confirm the closed form for lambda_pm.. 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: The two-cycle alternating superoperator S(pi/4,gamma,pi/2) S(pi/4,gamma,pi) has exactly three non-zero eigenvalues across a 47-point gamma grid (the next-largest discarded modulus is ~1.6e-8 numerical noise, well below TOL=1e-6): lambda_ss=+1, lambda_+ and lambda_-. The numeric lambda_+ and lambda_- match the closed form lambda_pm=(1/4)(1 +/- 3 sqrt(1-(2/9)[2+cos^4(gamma)] sin^2(2 gamma))) to <=1.8e-15 (lambda_+) and <=5.6e-16 (lambda_-) over the whole grid; a sympy spot-check at gamma=0.23pi gives formula 0.77675852 vs numeric 0.77675852. Tolerance 1e-8; satisfied. -> verified.