Reciprocal Evidence Cross Scans

Structure-Factor Square Scan

Three signed rows make the amplitude-to-intensity square visible. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Row 1: signed amplitude squares to intensity

The signed row has amplitude 2. Squaring that amplitude gives intensity 4; this is why signs are settled before brightness is compared.

F=1+(−1)+1+1=2I=F2=4F=1+(-1)+1+1=2\quad I=F^2=4
X-ray structure factorA sign-only structure-factor source is checked before ratio or absence use.termtermtermtermsigned sumF=2I=4

Row 2: signed amplitude squares to intensity

The signed row has amplitude 4. Squaring that amplitude gives intensity 16; this is why signs are settled before brightness is compared.

F=1+1+1+1=4I=F2=16F=1+1+1+1=4\quad I=F^2=16
X-ray structure factorA sign-only structure-factor source is checked before ratio or absence use.termtermtermtermsigned sumF=4I=16

Row 3: signed amplitude squares to intensity

The signed row has amplitude 6. Squaring that amplitude gives intensity 36; this is why signs are settled before brightness is compared.

F=1+1+1+1+1+1=6I=F2=36F=1+1+1+1+1+1=6\quad I=F^2=36
X-ray structure factorA sign-only structure-factor source is checked before ratio or absence use.termtermtermtermtermtermsigned sumF=6I=36