of the SQM model is $a \pmod 2$.

Although the integer $a$ is not a deformation invariant of the degree-$1$ SQM model, the mod-2 index $a\pmod 2$ is. To explain why, we can repeat the logic from §\[sec.noncompact\] to reinterpret a deformation of a degree-$n$ SQM model as a mildly-noncompact degree-$(n+1)$ SQM model: promote the deformation parameter to a dynamical supersymmetric multiplet; the fermion in this multiplet contributes $+1$ to the degree of the model. The upshot is that any deformation of a degree-$n$ SQM model will add or subtract to the ground states $V$ some $\operatorname{Cliff}(n+1,{{\mathds}R})$-module (thought of as a $\operatorname{Cliff}(n,{{\mathds}R})$-module).

But the even subalgebra of $\operatorname{Cliff}(2,{{\mathds}R})$ is isomorphic to ${{\mathds}C}$ thought of as a real algebra.[^21] Because ${{\mathds}C}$ is a field, $\operatorname{Cliff}(2,{{\mathds}R})$ is irreducible as a module over itself. We will call this irreducible module ${{\mathds}C}^{1|1}$. It has even graded dimension when restricted to $\operatorname{Cliff}(1,{{\mathds}R})$, since $\dim_{{\mathds}R}{{\mathds}C}$ is even, and so adding or subtracting it to $V = {{\mathds}R}^{a|a}$ will not change the value of $a \pmod 2$. This is why the mod-2 index of a degree-$1$ SQM model is a deformation invariant.

The same logic also defines a deformation-invariant mod-2 index of a degree-$2$ SQM model. The 