C013 - Eq. (2) reduces to a pure S_{x,e}^2 coupling at the loop-closing times t = 2 n pi / delta...
Verdict: verified
Location: Experiment
Type / expected artifact: math / math
Claim: Eq. (2) reduces to a pure S_{x,e}^2 coupling at the loop-closing times t = 2 n pi / delta (n in Z), for which Phi = n pi eta^2 Omega^2 / (2 delta^2).
Models: extraction claude-opus-4-8; verification gpt-5; verification_chain claude-opus-4-8 -> gpt-5; verdict_chain verified -> verified.
Source location(s): source/main.tex:115-120 (Experiment).
Conclusion
t=2 n pi/delta gives alpha=0 (loop closes) and Phi=n pi eta^2 Omega^2/(2 delta^2), matching the paper exactly. Verified symbolically (sympy, integer n).
Verification details
Derivation excerpt: From C012, $\alpha(t)=-i\frac{\eta\Omega}{\delta}e^{-i\delta t/2}\sin(\delta t/2)$ and $\Phi(t)=\frac{\eta^2\Omega^2}{4\delta^2}(\delta t-\sin\delta t)$.
Executable rerun: sympy_check.py exited 0 in 0.583s; log verification/C013/attempts/R002/sympy_check.log.
Output excerpt:
alpha(2 n pi/delta) = 0 -> zero: True
Phi(2 n pi/delta) = pi*Omega**2*eta**2*n/(2*delta**2)
Phi claim = pi*Omega**2*eta**2*n/(2*delta**2)
Phi match: True