A wrong finite reference can cancel the same signal. 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 wrong reference cancels the products

With reference 1, 1, -1, -1, the products are 1, -1, -1, 1.

1+1+1+1=01+-1+-1+1=0
Wrong referenceThe product ledger cancels exactly.signal=1,-1,1,-1reference=1,1,-1,-1products=1,-1,-1,1correlation=0acceptedBit=0 bit

Zero correlation is rejected

Correlation 0 gives accepted bit 0 for this finite gate.

acceptedBit=0\text{acceptedBit}=0
Rejected correlationNo continuous phase detector is implied.signal=1,-1,1,-1reference=1,1,-1,-1products=1,-1,-1,1correlation=0acceptedBit=0 bit