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Generation of a maximally entangled state using collective optical pumping

verification/C082/attempts/R002/review.md

Round 2 verification audit for C082

Model: gpt-5

Claim: Identifying |ee> as the excited subspace and applying the effective-operator formalism in the drive-(C) dressed basis |chi_0>,|chi_pm> yields the effective Hamiltonian Eq. (S15) and effective jump operators Eq. (S16) with constants C_0 = sqrt(2) J/(-i kappa), C_pm = J/(-/+ Omega_C - i kappa).

Source alignment: source/supp_content.tex:200-239 (Eqs. (S14-S17))

Prior official verdict: partial with failure_reason None.

Executable evidence: run.py. Sandbox rerun logs: run.log.

Independent audit: I scanned the copied script for imports/shared helper dependencies and reran it through the sandbox. The code is self-contained in this attempt directory and targets the claim strategy: Apply the Reiter-Sorensen effective-operator formalism to H_s and the jump operators and confirm the dressed-state couplings, effective jumps, and the C_0, C_pm constants.. I checked the relevant family model rather than relying only on exit status; the rerun is treated as one reproducibility input.

Decision: Round 2 verdict is partial with failure_reason None and limitations ['paper_text_only_reimplementation']. Notes: Reiter-Sorensen reduction (heavy analytic). Verified tractable structure: dressed states chi_0,chi_pm (Eq S14) are orthonormal; under drive-(C) generator they have eigenvalues 0 (chi_0) and +/-Omega_C (chi_pm) -> the denominators -i kappa and -/+Omega_C - i kappa. =sqrt2, =1 -> numerators sqrt2 J and J. No-jump rate out of |ee| =2 kappa -> H_NH imaginary part -i kappa. Hence C_0=sqrt2 J/(-i kappa), C_pm=J/(-/+Omega_C - i kappa) (Eq S17) reproduced. Full S15/S16 operator algebra consistent but not re-derived term-by-term; capped at partial.