A threshold position scan holds the raw readout signal fixed at 6, between calibrated endpoints 0 and 10, and moves only the decision threshold across three rows: threshold 3 reads the fixed signal as one, threshold 6 ties exactly and reads as repeat, and threshold 9 reads the same fixed signal as zero, exactly for the stated toy threshold rule. Real calibration has to choose this decision boundary carefully, since the same physical reading can be classified differently depending only on where the threshold was set.
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⟩
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.
T369resultonerepeatzero
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.