A failed audit is easiest to see by following the repaired word all the way
to the end. Here syndrome 01 and correction index 2 claim a repair, but the
word lands at 000 instead of the protected code word, so the toy accepted bit
is 0; real double-error flags depend on repeated noisy checks.
A double-error repair claim must fail when the corrected word drifts. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
The rejected audit carries the failed correction
The audit sees syndrome 01 and correction index 2, but the repaired word is 000.
s=01c=2wfixed=000
The final audit state is rejected
Because the corrected word does not match the code word, the accepted bit is 0.