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Generation of a maximally entangled state using collective optical pumping

verification/C045/attempts/R002/claim_report.md

C045 - In the alternating-drive scheme the protocol converges optimally at gamma^opt ~= 0.23 pi...

Verdict: partial Location: Supp. Mat. S1 Type / expected artifact: numeric / numeric Claim: In the alternating-drive scheme the protocol converges optimally at gamma^opt ~= 0.23 pi with rate 1/N_0^opt = -(1/2) log(lambda_+^opt) ~= 1/7.92 per cycle; for the experimentally measured gamma ~= 0.31 pi the rate is 1/10.35 per cycle. Models: extraction claude-opus-4-8; verification gpt-5; verification_chain claude-opus-4-8 -> gpt-5; verdict_chain partial -> partial. Limitations: paper_text_only_reimplementation, rounded_input_sensitivity. Source location(s): source/supp_content.tex:56 (Supp. Mat. S1).

Conclusion

Round-2 audit preserves partial but removes the hard mismatch flag. The closed-form lambda_+(gamma) was read and rerun; it agrees with the full two-cycle superoperator. The optimum is gamma=0.2310pi and N0=7.9165, matching the paper. At the literal rounded gamma=0.31pi the rate is 1/10.6855, but gamma=0.305pi gives N0=10.3096, consistent with the printed 1/10.35. Because the paper labels gamma as approximate, this is a rounded-input sensitivity rather than a hard contradiction.

Verification details

Executable rerun: run.py exited 0 in 0.622s; log verification/C045/attempts/R002/run.log.

Output excerpt:

gamma=0.23pi  formula lam+=0.776759  numeric lam+=0.776759
gamma=0.31pi  formula lam+=0.829304  numeric lam+=0.829304
optimum: gamma_opt=0.2310pi  lambda_+^opt=0.776749
  optimal rate = 1/N0 = 0.126319 per cycle = 1/7.9165
  paper: gamma_opt~0.23pi, rate~1/7.92  -> match: True
measured gamma=0.31pi: rate = 1/10.6855 per cycle
  paper says 1/10.35  -> computed 1/10.69  relative diff = 3.2%
DONE

Supporting files