Tr[(-1)^F e^{-βH}] — counting ground states protected by topology
The Witten index W = Tr[(-1)^F e^{-βH}] counts bosonic minus fermionic zero-energy states. For the SUSY quantum mechanics H = ½{Q,Q†}, paired states (E>0) cancel in pairs. Only unpaired ground states contribute. W is an integer topological invariant — robust to smooth deformations that preserve SUSY.