C004 - Drive (B) repumps population from |e> to the qubit states with branching ratios parameter...
Verdict: verified
Location: Dissipation scheme
Type / expected artifact: math / math
Claim: Drive (B) repumps population from |e> to the qubit states with branching ratios parameterized by p_{e->down}/p_{e->up} = tan^2(gamma).
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:106-107 (Dissipation scheme).
Conclusion
p_e->down=sin^2(gamma), p_e->up=cos^2(gamma). Symbolic p_down/p_up - tan^2(gamma)=0 and p_down+p_up=1 (sympy). Numeric over gamma in [0,pi/2): ratio=tan^2(gamma), sweeps full range [0,inf); Kraus completeness sum E^dag E=I. -> verified.
Verification details
Derivation excerpt: Drive B is a single-ion repump channel taking $|e\rangle$ to the qubit states with probabilities $p_{e\to\downarrow}$ and $p_{e\to\uparrow}$. The parameterization (Supp. Mat. S1, protocol Kraus operators) is $$p_{e\to\downarrow}=\sin^2\gamma,\qquad p_{e\to\uparrow}=\cos^2\gamma.$$
Executable rerun: sympy_check.py exited 0 in 0.713s; log verification/C004/attempts/R002/sympy_check.log.
Output excerpt:
symbolic p_dn/p_up - tan^2(gamma) = 0
symbolic p_dn + p_up = 1
gamma/pi, p_dn, p_up, sum, ratio, tan^2:
0.00 0.00000 1.00000 1.00000 0.00000 0.00000
0.10 0.09549 0.90451 1.00000 0.10557 0.10557
0.25 0.50000 0.50000 1.00000 1.00000 1.00000
0.40 0.90451 0.09549 1.00000 9.47214 9.47214
0.49 0.99901 0.00099 1.00000 1012.54524 1012.54524
Kraus completeness sum E^dag E = I : True
ALL_CHECKS_PASS = True