A reciprocal step scale scan checks the same four bin indexes, zero through three, against three different calibrated reciprocal steps: step 1 per metre gives bin values 0, 1, 2, 3; step 2 gives 0, 2, 4, 6; step 3 gives 0, 3, 6, 9, all exactly for the stated toy detector rule. Chapter two checked one fixed step once; this scan shows the same index list means a different physical reciprocal-space scale depending entirely on the calibrated step, so an index alone never tells the whole story without its calibration.
The same four checked bin indexes map to three different physical reciprocal-space scales depending on the calibrated step. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Chapter two's single training row fixed the step
Chapter two checked one reciprocal step and its four bin values once. The same index list zero through three can be recalibrated to a different step: here 1 per metre.
qi=iΔq,Δq=11/m
The same index list gives three different bin scales
Every row checks the same four indexes, zero through three. Only the calibrated step changes, so a reader has to know the step to know what a bin index actually means physically.