Boundary Depth Scans

Lock-In Correlation Sign Three-Row Scan

Lock-in acceptance is scanned through positive, zero, and negative correlation. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A matching reference gives positive correlation

Four positive products make correlation four, so the lock-in row is accepted.

4>0⇒14>0\Rightarrow1
Positive lock-in rowProducts and accepted bit are source-bound.signal=1,-1,1,-1reference=1,-1,1,-1products=1,1,1,1correlation=4acceptedBit=1 bit

Zero correlation is not accepted

A flat reference cancels the signed products exactly to zero.

0≯0⇒00\not>0\Rightarrow0
Zero-correlation rowThe strict positive gate rejects zero.signal=1,-1,1,-1reference=1,1,1,1products=1,-1,1,-1correlation=0acceptedBit=0 bit

An inverted reference makes the sum negative

The final row is below the same threshold, not just mismatched by name.

corraccepted4100−40\begin{array}{c|c}\text{corr}&\text{accepted}\\4&1\\0&0\\\mathbin{-}4&0\\\end{array}
Negative lock-in rowChanging the reference changes every product.signal=1,-1,1,-1reference=-1,1,-1,1products=-1,-1,-1,-1correlation=-4acceptedBit=0 bit