An averaging gate turns a row of residuals into one squared-residual budget, then compares that budget with a fixed limit. The useful picture is the boundary: zero residual passes easily, a budget exactly equal to the limit still passes, and one more unit of budget fails.
The scan uses five readings with budgets 0, 9, and 10 against limit 9, giving accepted bits 1, 1, and 0 for the stated toy noise ledger. Real measurements still carry baseline drift, sensor calibration, sampling resolution, and residual-distribution uncertainty.
A residual budget is scanned below, at, and above the acceptance limit. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Zero residual budget passes the gate
All five readings match the target, so the squared budget is zero.
0≤9⇒1
Equality at the limit still passes
One reading at three volts gives budget nine, exactly at the limit.
9≤9⇒1
One extra residual square rejects the row
Adding a one-volt residual raises the budget to ten, so the row fails.