Boundary, rejection, and re-admission rows show the load gate as an energy inequality. 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 four-newton load exactly spends twelve joules
Available energy is 12 joules and the step is 3 metres. A 4 newton load requires 12 joules, so the accepted bit is 1.
4⋅3=12≤12
Five newtons asks for more energy than is available
Keep available energy at 12 joules and keep the step at 3 metres. A 5 newton load requires 15 joules, so the accepted bit drops to 0.
5⋅3=15>12
Raising available energy accepts that same five-newton load
Now available energy is 15 joules for the same 3 metre step. The 5 newton load still requires 15 joules, and the accepted bit returns to 1.