The four-point comparison inequality conjecture for Atiyah–Sutcliffe quantities

For four distinct points $x_1,x_2,x_3,x_4$ in $\mathbb{R}^3$, let the expressions denoted by

$$and$$

in the source be the corresponding angular quantities. Four-point comparison inequality conjecture. The left-hand side of

is at least twice the \left-hand side of

.

The paper reports numerical verification for several million random tetrahedra, but gives no general proof.