Round 2 verification audit for C001

Model: gpt-5

Claim: The singlet Bell state is defined as |Psi^-> = (|up,down> - |down,up>)/sqrt(2).

Source alignment: source/main.tex:92-92 (Introduction)

Prior official verdict: verified with failure_reason None.

Executable evidence: sympy_check.py. Sandbox rerun logs: sympy_check.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: Confirm this is a valid normalized maximally entangled two-qubit state and that it is the antisymmetric (singlet) combination used throughout the paper.. 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: Singlet |Psi^-> = (|up,down>-|down,up>)/sqrt(2). Verified normalized (norm=1.0), antisymmetric (SWAP|psi>=-|psi>), maximally entangled (reduced rho1=I/2, S=ln2=0.6931), total-spin-0 (Sx,Sy,Sz annihilate it). Clean math fact -> verified.