The filled boundary case has zero empty slots. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
The same slot ledger can be completely filled
The toy band again has 8 slots.
s l o t s = 4 ⋅ 2 = 8 slots=4\cdot 2=8 s l o t s = 4 ⋅ 2 = 8 Filled band slots Every displayed count is checked. sites=4 statesPerSite=2 electrons=8 slots=8 filled=8 empty=0 occupancy=filled
Eight electrons fill all eight slots
The filled count is 8 and the empty count is 0.
f i l l e d = 8 , e m p t y = 0 , o c c u p a n c y = f i l l e d filled=8,\quad empty=0,\quad occupancy=\mathrm{filled} f i ll e d = 8 , e m pt y = 0 , occ u p an cy = filled Filled occupancy Filled means no empty slots in this toy ledger. sites=4 statesPerSite=2 electrons=8 slots=8 filled=8 empty=0 occupancy=filled