Round 2 verification audit for C003

Model: gpt-5

Claim: The collective excitation unitary U_A(Phi) = exp(-i Phi S_{x,e}^2), with S_{x,e}=sigma_{x,down e} tensor 1 + 1 tensor sigma_{x,down e}, provides full transfer from |down,down> to |ee> for Phi = pi/4.

Source alignment: source/main.tex:102-106 (Eq. (1))

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: Construct S_{x,e} on the {|down>,|e>} subspace, exponentiate exp(-i (pi/4) S_{x,e}^2), and verify ||^2 = 1 at Phi=pi/4.. 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: U_A(Phi)=exp(-i Phi S_xe^2). Computed ||^2 = 1.0 (paper: full transfer =1). Closed form sin^2(2 Phi) confirmed over Phi scan; U_A unitary. Exact match. -> verified.