Round 2 verification audit for C054

Model: gpt-5

Claim: In the limit |alpha(t)|<<1, residual spin-motion entanglement creates a correlated bit-flip with probability p = |alpha(t)|^2, with Kraus operator I_e X_e + X_e I_e.

Source alignment: source/supp_content.tex:84-84 (Supp. Mat. S2)

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: Expand the spin-dependent displacement to first order in alpha(t) and confirm the single-quantum branch carries probability |alpha(t)|^2 with the stated correlated bit-flip structure.. 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', 'normalization_convention', 'oscillator_truncation']. Notes: Expanded D=exp(alpha S_x a^dag - alpha S_x a), S_x = X_e^(1)+X_e^(2), on |dd>|0> (qutip, Fock cutoff 20). One-quantum Kraus branch K_1 = <1|D|0> = alpha(I_eX_e + X_eI_e)|dd> exactly to first order (ratio 0.99998), confirming the correlated bit-flip Kraus op I_eX_e+X_eI_e and the single-quantum mechanism. Its population scales as |alpha|^2 (||K_1|dd>||^2/|alpha|^2 -> 2.000 = ||S_x|dd>||^2 as alpha->0); the absolute factor 2 arises because the collective S_x on |dd> has two single-ion flip terms (paper's p=|alpha|^2 is the per-ion single-quantum probability). Structure and |alpha|^2 scaling confirmed. Partial: paper-text-only model, per-ion-vs-collective alpha normalization, small truncation.