Audit Contract Boundary Three-Row Scan - Quantum Mechanics V: Error Correction and Stabilizer Checks Step by Step

An audit contract boundary checks that both the lookup correction and the data-error round agree before the repaired word is accepted, so missing either gate fails the audit. The three rows give contract scores 0+1-2 = -1, 0+1-2 = -1, and 1+1-2 = 0 (fail, fail, pass) exactly for the stated toy syndrome ledger; real stabilizer measurements have readout errors, repeated-round reliability, calibration, and hardware noise.

A stabilizer audit accepts only when lookup and round contracts both pass. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Audit acceptance needs the lookup and the round contract

The first row has a repeated syndrome, but its lookup repair is rejected.

m=a_{\text{lookup}}+a_{\text{round}}\mathbin{-}2

A second alias also fails the lookup contract

The second rejected row uses a different syndrome, but its repaired word still misses the code word.

\begin{array}{c|c|c|c}a_{\text{lookup}}&a_{\text{round}}&m&\text{gate}\\0&1&-1&\text{fail}\\0&1&-1&\text{fail}\\1&1&0&\text{pass}\\\end{array}

Only both source contracts pass the audit

The final row has a repaired word and a data-error round, so the audit accepts.

m=0\quad \text{pass}