NFOP2 properties are quadratic-atomic or contain a generalized Green–Sanders example

Let $\mathcal{P}$ be an elementary $p$-group property, and let $\mathrm{NFOP}_2$ mean that it has no functional order property of order two. A property is quadratically atomic when it satisfies the paper's quadratic atomicity condition, and it contains a generalized Green–Sanders example when it contains one of the stated generalized obstructions. NFOP2 dichotomy conjecture. If an epGP $\mathcal{P}$ is $\mathrm{NFOP}_2$, then it is either quadratically atomic or contains a generalized Green–Sanders example. This is proposed because the Green–Sanders example is $\mathrm{NFOP}_2$ but not quadratically atomic; the conjecture remains unresolved in the supplied text.