C049 - The 16 error operators are M_{i,j} = exp(-i (pi/2) sigma_{i,down e} tensor sigma_{j,down...
Verdict: verified
Location: Supp. Mat. S2
Type / expected artifact: math / math
Claim: The 16 error operators are M_{i,j} = exp(-i (pi/2) sigma_{i,down e} tensor sigma_{j,down e}) with i,j in {0,x,y,z} (sigma_0=I), defined local when i=0 or j=0 and global otherwise.
Models: extraction claude-opus-4-8; verification gpt-5; verification_chain claude-opus-4-8 -> gpt-5; verdict_chain verified -> verified.
Source location(s): source/supp_content.tex:60-64 (Supp. Mat. S2).
Conclusion
Round-2 audit corrects an overbroad round-1 note while preserving the verified verdict. The script verifies all 16 M_{i,j}=exp[-i(pi/2) sigma_i tensor sigma_j] are finite and unitary, their {down,e}^{otimes2} block equals -i sigma_i tensor sigma_j, and the local/global count is 7 local (i=0 or j=0, including identity) and 9 global. The old statement that every |up>-containing basis state is invariant is false for local channels such as I tensor X; that property is not part of the claim. The operator definition and classification claimed in the paper are verified.
Verification details
Executable rerun: run.py exited 0 in 0.531s; log verification/C049/attempts/R002/run.log.
Output excerpt:
M_II: local unitary=True block=-i*(s_i(x)s_j)=True
M_IX: local unitary=True block=-i*(s_i(x)s_j)=True
M_IY: local unitary=True block=-i*(s_i(x)s_j)=True
M_IZ: local unitary=True block=-i*(s_i(x)s_j)=True
M_XI: local unitary=True block=-i*(s_i(x)s_j)=True
M_XX: global unitary=True block=-i*(s_i(x)s_j)=True
M_XY: global unitary=True block=-i*(s_i(x)s_j)=True
M_XZ: global unitary=True block=-i*(s_i(x)s_j)=True
M_YI: local unitary=True block=-i*(s_i(x)s_j)=True
M_YX: global unitary=True block=-i*(s_i(x)s_j)=True