Signed amplitude paths can reinforce or cancel before probability is computed. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Interference adds amplitudes before squaring

The rendered row uses path amplitudes 1/5 and negative 2/5. Add the signed amplitudes first; square only after the sum is known.

1525=15\frac{1}{5}-\frac{2}{5}=-\frac{1}{5}
Signed interferenceThe negative path reduces the amplitude sum.1/5 + -2/5= -1/5P = 1/25amplitude sum

The smaller signed sum gives a smaller probability

After cancellation, the result amplitude has probability 1/25. This is why a sign can matter even when a direct sign-only measurement did not change a probability bar earlier.

P=(15)2=125P=\left(-\frac{1}{5}\right)^2=\frac{1}{25}
Interference probabilityProbability is attached to the summed amplitude.1/5 + -2/5= -1/5P = 1/25amplitude sum

Three signed sums show constructive and destructive cases

The first and third rows are constructive sums. The middle row uses the same magnitudes as the first row but flips one sign, so the probability drops instead of growing.

aleftarightAP152535925152515125352511\begin{array}{c|c|c|c}a_{\text{left}}&a_{\text{right}}&A&P\\\frac{1}{5}&\frac{2}{5}&\frac{3}{5}&\frac{9}{25}\\\frac{1}{5}&\frac{-2}{5}&\frac{-1}{5}&\frac{1}{25}\\\frac{3}{5}&\frac{2}{5}&1&1\end{array}
Interference sign scanThe rendered row is the destructive middle row.1/5 + -2/5= -1/5P = 1/25amplitude sum

This is a finite amplitude audit, not a wave animation

The lesson stays inside the finite qubit model. No continuous wave equation is solved here; the honest claim is the checked addition of exact signed amplitudes.

A=aleft+aright,P=A2A=a_{\text{left}}+a_{\text{right}},\quad P=A^2
Interference auditThe visible amplitude sum is the source of the probability.1/5 + -2/5= -1/5P = 1/25amplitude sum