Classification conjecture for positive viscosity solutions of the conformally invariant equation

Let $(f,\Gamma)$ satisfy conditions (01)--(04), and let $0<v\in C^0_{\mathrm{loc}}(\mathbb{R}^n)$ be a viscosity solution of the equation (B0). Write the family referred to as (vform) as

$$v(x)=\left(\frac{a}{b^2+|x-\bar x|^2}\right)^{\frac{n-2}{2}},$$

for parameters to be specified by the equation. Classification conjecture. Every such $v$ has the form (vform) for some $\bar x\in\mathbb{R}^n$ and some positive constants $a$ and $b$. This conjecture seeks a complete classification of positive viscosity solutions; the supplied source does not state a resolution, so its status remains open.