C048 - Fig. (lambda_const_vs_altern): comparison of lambda_max for constant versus alternating d...
Verdict: partial
Location: Supp. Mat. S1, Fig.
Type / expected artifact: plot / figure (lambda_const_vs_altern.pdf)
Claim: Fig. (lambda_const_vs_altern): comparison of lambda_max for constant versus alternating drive (C) as a function of branching angle gamma, using lambda_max = lambda_+^{1/2} for the alternating case.
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:49-54 (Fig. lambda_const_vs_altern).
Conclusion
Reproduced lambda_max(gamma) for constant vs alternating drive (C) using lambda_max=lambda_+^{1/2} for the alternating case. Constant min 0.8770 at gamma=0.221 pi (1/7.62); alternating min 0.8813 at gamma=0.231 pi (1/7.92), matching paper optima. Closed-form lambda_+ matches numeric second_eigmag to 1.6e-15. Curves and y-range match paper. Theory-reproducible plot; Tier-A visual match only -> caps at partial.
Verification details
Executable rerun: run.py exited 0 in 10.405s; log verification/C048/attempts/R002/run.log.
Output excerpt:
constant: min lambda_max=0.8770 at gamma=0.221 pi -> 1/N0=7.617 (paper opt gamma~0.22pi, 1/7.62)
alternating(closed): min lambda_max=0.8813 at gamma=0.231 pi -> rate -0.5 log lam_+ = 0.1263 ~ 1/7.916 (paper opt gamma~0.23pi, 1/7.92)
max |closed - numeric| over grid = 1.55e-15
wrote figure.png
Plot evidence:
Visual comparison notes: - Reproduced lambda_max(gamma) for constant drive (C) (solid) and alternating odd/even drive (C) (dashed, using lambda_max=lambda_+^{1/2}) matches the paper: both curves -> 1 at gamma=0 and gamma=pi/2, with a single minimum near gamma~pi/4 and the solid (constant) curve dipping slightly below the dashed (alternating) curve near the minimum. - Constant-drive minimum lambda_max=0.8770 at gamma=0.221 pi (rate 1/7.62); alternating minimum lambda_max=0.8813 at gamma=0.231 pi (rate -0.5 log lambda_+ = 1/7.92), matching paper optima (0.22 pi / 1/7.62 and 0.23 pi / 1/7.92). - Closed-form lambda_+ (Eq. eigenval_alternate_cycles) agrees with the numeric second_eigmag of S(pi/4,gamma,pi/2)S(pi/4,gamma,pi) to 1.6e-15 over the whole grid. - Same y-range (~0.87-1.0) as the paper. Tier-A visual comparison only; no raw data and no digitization.
