Round 2 verification audit for C067

Model: gpt-5

Claim: Turning every odd drive (C) into a pi-pulse acts as a spin-echo that coherently reverses the differential-phase error, returning the population to |Psi^-> at the end of each even cycle.

Source alignment: source/supp_content.tex:127-127 (Supp. Mat. S4)

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: Model the |Psi^-><->|Psi^+> coupling with an interleaved pi flip and confirm the accumulated phase cancels over an odd/even cycle pair.. 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: Spin-echo cancellation confirmed analytically and numerically. Per-drive-(A) error E(phi)=diag(exp(-i phi/2),exp(+i phi/2)) on {|up,dn>,|dn,up>}; collective drive-(C) pi-pulse X=sx(x)sx swaps them. Echo identity X E(phi) X = E(-phi) holds on the ground-state subspace (verified phi in {0.3,1.0,2.137,3.0}). Over an odd/even cycle pair U=E(phi) X E(phi)=X E(-phi) E(phi)=X, so phase cancels exactly and X|Psi->=-|Psi->: system returns to |Psi-> with P(|Psi->)=1.000000, leakage ~1e-33 independent of phi. Without echo, two plain A drives leak ~0.71 to |Psi+> at phi=2.137. Clean mathematical fact -> verified.