X-Ray Source Control Depth Scans

Systematic Absence Source Variant Scan

A zero peak is accepted only through its checked zero structure-factor source. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Absence evidence starts from a zero signed source

The absence helper accepts only when amplitude and intensity are exactly zero.

F=0I=0F=0\quad I=0
X-ray systematic absenceA checked zero amplitude is the only accepted absence claim.termtermtermtermsigned sumF=0I=0F=0I=0accepted=1

Three signed rows all cancel before intensity

Different sign patterns can make the same zero peak, but each one must be cited as its own source.

sign rowFI1+(−1)001+(−1)+1+(−1)001+1+(−1)+(−1)00\begin{array}{c|c|c}\text{sign row}&F&I\\1+(-1)&0&0\\1+(-1)+1+(-1)&0&0\\1+1+(-1)+(-1)&0&0\\\end{array}

The middle row is still an exact absence

The four-term row cancels to amplitude 0 and intensity 0; it is not a weak nonzero peak.

F=1+(−1)+1+(−1)=0I=0F=1+(-1)+1+(-1)=0\quad I=0
X-ray systematic absenceA checked zero amplitude is the only accepted absence claim.termtermtermtermsigned sumF=0I=0F=0I=0accepted=1