A gradient window alignment checks that the receive window fits inside the required gradient coverage interval, so the readout does not miss the intended encoding period. Both the required gradient window and the receive window span 2 to 8 s, so the alignment closes exactly for the stated toy timing ledger; real gradient systems have settling time, slew limits, synchronization drift, and calibration uncertainty.
A receive window is valid only while the required control window covers it. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
A receive window needs coverage
The required gradient window starts at 2 s and ends at 8 s.
required=[2s,8s]
Receive sits inside the required window
The receive window also runs from 2 s to 8 s, so the alignment closes. This does not model real gradient slew.