A structure factor adds signed scattering contributions before squaring, so the signs of individual terms change the final intensity even when each has unit magnitude. The contributions plus, minus, plus, plus sum to A = 1 - 1 + 1 + 1 = 2, giving intensity 2 squared = 4 exactly for the stated toy structure ledger; real structure factors need phases, atom positions, scattering strengths, noise, and measurement uncertainty.
A sign-only structure factor adds before it is squared. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Signed contributions add before intensity
The signed contributions are plus, minus, plus, plus. Their exact amplitude is 2.
A=1+−1+1+1=2
Intensity squares the amplitude
The intensity is 2 squared, so the exact training intensity is 4.