Round 2 verification audit for C053

Model: gpt-5

Claim: For both ions in the {down,e} subspace, U_i(epsilon) creates an error with probability p ~= 2 (epsilon/2)^2 for p<<1, so the process is parametrized by epsilon = sqrt(2 p).

Source alignment: source/supp_content.tex:82-82 (Supp. Mat. S2)

Prior official verdict: verified 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 U_x(epsilon) acting on |down,down> to second order and confirm the single-flip probability is 2(epsilon/2)^2 = epsilon^2/2... i.e. p = 2(epsilon/2)^2 and epsilon=sqrt(2p).. 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 verified with failure_reason None and limitations []. Notes: P(exactly one ion flipped) for U_x(eps)|dd> = 2 sin^2(eps/2) cos^2(eps/2) = eps^2/2 - eps^4/6 + O(eps^6) (sympy); leading coeff 1/2 => p ~= 2(eps/2)^2 = eps^2/2, so eps=sqrt(2p). Numeric eps=0.05 -> 1.2490e-3 (paper hint 1.25e-3); p_one/(eps^2/2) -> 1 as eps->0; round-trip eps=sqrt(2p) recovers p. Clean asymptotic math fact -> verified.