An interference sign scan adds signed path amplitudes before squaring, so flipping one sign can shrink the result probability even when the magnitudes stay the same. The three rows give (1/5, 2/5) with sum 3/5 and probability 9/25, (1/5, -2/5) with sum -1/5 and probability 1/25, and (3/5, 2/5) with sum 1 and probability 1 exactly for the stated toy amplitude ledger; real interferometers and qubit experiments have visibility limits, calibration drift, noise, alignment, and finite-shot uncertainty.
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.
51−52=−51
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=(−51)2=251
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.
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.