Gomory–Johnson's facet conjecture for the infinite group problem

Let $f\in(0,1)$ be fixed, and consider the infinite group problem with variables $s_r\in\mathbb{Z}_+$ for $r\in[0,1)$, finite support, and the equality constraint

$$\sum_{r\in[0,1)}rs_r=f,$$

where additions are modulo $1$. A nonnegative function $\pi:[0,1)\to\mathbb{R}$ with $\pi(0)=0$ is valid when every feasible solution satisfies $\sum_{r\in[0,1)}\pi(r)s_r\geq1$. A valid inequality is a facet if its equality solutions are not contained in those of any distinct valid inequality. A function is piecewise linear if it is affine on finitely many intervals of a finite partition of $[0,1)$. Facet conjecture. Every continuous facet for the infinite group problem is piecewise linear. The conjecture was disproved in the paper by exhibiting a continuous facet that is not piecewise linear.