C046 - Fig. (discrete_eigenvalue): the second dominant eigenvalue lambda_max of S(pi/4,gamma,the...
Verdict: partial
Location: Supp. Mat. S1, Fig.
Type / expected artifact: plot / figure (discrete_eigenvalue.png)
Claim: Fig. (discrete_eigenvalue): the second dominant eigenvalue lambda_max of S(pi/4,gamma,theta) as a function of (gamma,theta), minimized at theta^opt ~= 0.72 pi, gamma^opt ~= 0.22 pi.
Models: extraction claude-opus-4-8; verification gpt-5; verification_chain claude-opus-4-8 -> gpt-5; verdict_chain partial -> partial.
Limitations: visual_match_only, paper_text_only_reimplementation.
Source location(s): source/supp_content.tex:29-34 (Fig. discrete_eigenvalue).
Conclusion
Reproduced lambda_max heatmap of S(pi/4,gamma,theta) (self-contained model) over (theta in [0,pi], gamma in [0,pi/2]). Grid minimum lambda_max=0.87697 at theta=0.717 pi, gamma=0.221 pi vs paper theta^opt~0.72 pi, gamma^opt~0.22 pi; rate -1/log(lambda_max)=7.617 vs paper 1/7.62. Heatmap structure and RdBu color scale match. Theory-reproducible plot; Tier-A visual match only -> caps at partial.
Verification details
Executable rerun: run.py exited 0 in 6.608s; log verification/C046/attempts/R002/run.log.
Output excerpt:
grid min lambda_max = 0.87697 at theta=0.717 pi, gamma=0.221 pi
N0_opt = -1/log(lambda_max) = 7.617
paper: theta_opt ~ 0.72 pi, gamma_opt ~ 0.22 pi, 1/N0 ~ 1/7.62
lambda_max range over grid: [0.8770, 1.0000]
wrote figure.png
Plot evidence:
Visual comparison notes: - Reproduced heatmap of lambda_max for S(pi/4,gamma,theta) over theta in [0,pi], gamma in [0,pi/2] matches the paper figure: same RdBu color scale (0.88-1.0), same red minimum lobe centred near theta~3pi/4, gamma~pi/4, and lambda_max -> 1 toward the grid edges. - Grid minimum lambda_max=0.87697 located at theta=0.717 pi, gamma=0.221 pi, matching the paper's stated optimum theta^opt~0.72 pi, gamma^opt~0.22 pi. - Implied convergence rate -1/log(lambda_max)=7.617 matches the paper's 1/N0~1/7.62. - Tier-A visual comparison only; no raw data and no digitization.
