Round 2 verification audit for C073

Model: gpt-5

Claim: The thresholding miscount is corrected via P(up,up) = [(1-p)P(2) - p P(1)]/(1-p-q) and P(up,down)+P(down,up) = [(1-q)P(2) - q P(1)]/(1-p-q), where p (q) is the probability that 1 (2) bright ions are recorded as 2 (1).

Source alignment: source/supp_content.tex:137-142 (Eqs. (S7-S8))

Prior official verdict: partial with failure_reason mismatch.

Executable evidence: sympy_check.py. Sandbox rerun logs: sympy_check.log.

Independent audit: I read the confusion-matrix inversion. S7 matches the inverse, but S8 as printed swaps P(1) and P(2) in the numerator and fails probability conservation. This is a source-level formula typo, so partial/mismatch remains.

Decision: Round 2 verdict is partial with failure_reason mismatch and limitations []. Notes: Eq.(S7) P(uu)=[(1-p)P(2)-pP(1)]/(1-p-q) verified exactly by inverting the confusion matrix [[1-p,q],[p,1-q]]. Eq.(S8) as printed [(1-q)P(2)-qP(1)]/(1-p-q) does NOT match the inverse; correct form is [(1-q)P(1)-qP(2)]/(1-p-q) (P1/P2 swapped). Paper's S7+S8 violates probability conservation; the correct pair conserves it. Likely a typo in S8 -> partial (mismatch on second equation).