Boundary and Invariant Scans

Period Law Mismatch Three-Row Scan

Three exact rows hold the ratio fixed while the law changes. 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 observed ratio is judged by the cited law

The observed ratio stays fixed; only the cited law constant changes, so the acceptance bit flips only for the matching row.

K=14T2R3=1020=12accept=0\begin{array}{c}K=\frac{1}{4}\\{T^{2}\over R^{3}}={10\over20}=\frac{1}{2}\\\text{accept}=0\end{array}
Period mismatch row oneThe same ratio is judged against a different law.lawConstant=1/4periodSquared=10radiusCubed=20ratio=1/2acceptedBit=0 bit

The same observed ratio is judged by the cited law

The observed ratio stays fixed; only the cited law constant changes, so the acceptance bit flips only for the matching row.

K=12T2R3=1020=12accept=1\begin{array}{c}K=\frac{1}{2}\\{T^{2}\over R^{3}}={10\over20}=\frac{1}{2}\\\text{accept}=1\end{array}
Period mismatch row twoThe same ratio is judged against a different law.lawConstant=1/2periodSquared=10radiusCubed=20ratio=1/2acceptedBit=1 bit

The same observed ratio is judged by the cited law

The observed ratio stays fixed; only the cited law constant changes, so the acceptance bit flips only for the matching row.

K=23T2R3=1020=12accept=0\begin{array}{c}K=\frac{2}{3}\\{T^{2}\over R^{3}}={10\over20}=\frac{1}{2}\\\text{accept}=0\end{array}
Period mismatch row threeThe same ratio is judged against a different law.lawConstant=2/3periodSquared=10radiusCubed=20ratio=1/2acceptedBit=0 bit