Asymmetric Calibration Scans

Threshold Position Three-Row Scan

the same signal, three verdicts

A fixed raw signal reads as one, repeat, or zero depending only on where the decision threshold was calibrated. 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 same raw signal can read as one

Chapter six scanned the signal at a fixed threshold. Here the signal stays fixed at 6 and only the threshold moves. With threshold 3, the fixed signal reads above it.

6>3⇒∣1⟩6>3\Rightarrow \lvert 1\rangle
Low threshold reads oneThe fixed signal sits above this low threshold.zero signal 0one signal 10threshold 3input 6 reads one

Threshold placement alone changes the verdict

The signal never changes across this scan. Only where the threshold was calibrated changes the result: below, on, or above the same fixed reading.

Tresult3one6repeat9zero\begin{array}{c|c}T&\text{result}\\3&\text{one}\\6&\text{repeat}\\9&\text{zero}\\\end{array}
Threshold on the signalThe middle threshold sits exactly on the fixed signal.zero signal 0one signal 10threshold 6input 6 reads repeat

A higher threshold reads the same signal as zero

With threshold 9, the same fixed signal now reads below it. Nothing about the measured signal changed; only the calibrated decision boundary did.

6<9⇒∣0⟩6<9\Rightarrow \lvert 0\rangle
High threshold reads zeroThe fixed signal now sits below this high threshold.zero signal 0one signal 10threshold 9input 6 reads zero