C006 - After N cycles the singlet error epsilon = 1 - F(|Psi^->) decays as epsilon proportional...
Verdict: verified
Location: Dissipation scheme
Type / expected artifact: math / math / sec:convergence_rate
Claim: After N cycles the singlet error epsilon = 1 - F(|Psi^->) decays as epsilon proportional to exp(-N/N_0).
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:108 (Dissipation scheme).
Conclusion
eps=1-F decays as exp(-N/N0). At optimal params (Phi=pi/4, gamma=0.221pi, theta=0.716pi), simulated eps(N) over N=0..40: log(eps) vs N linear (R^2=0.99999999), fitted N0=7.617 = independent second-eigenvalue prediction (lambda2=0.877, N0=7.617) = paper N0~7.62 (<0.1%). Math fact from model superoperator. -> verified.
Verification details
Derivation excerpt: One protocol cycle is a trace-preserving linear map on density matrices, represented by the superoperator $S=S_C S_B S_A$ acting on $\mathrm{vec}(\rho)$. Its spectrum $\{\lambda_k\}$ satisfies $|\lambda_k|\le1$. The unique steady state is the singlet, $\lambda_0=1$ with right eigenvector $\mathrm{vec}(|\Psi^-\rangle\langle\Psi^-|)$ (verified in C008). Order the remaining eigenvalues by magnitude; let $\lambda_2$ be the largest with $|\lambda_2|<1$.
Executable rerun: run.py exited 0 in 0.508s; log verification/C006/attempts/R002/run.log.
Output excerpt:
N, eps=1-F (first 12):
0 7.500000e-01
1 6.895522e-01
2 6.124540e-01
3 5.309389e-01
4 4.662210e-01
5 4.094630e-01
6 3.587788e-01
7 3.146613e-01
8 2.759768e-01