Equidistribution conjecture for slopes of primes represented by homogeneous polynomials

Let $f(x,y)$ be a homogeneous polynomial of degree $n$, and define

$$F(t)=\int_0^t\frac{dy}{[\sqrt[n]{f(1,y)}]^2}.$$

Let $C_f(t_1,t_2,M)$ count primes $p=f(a,b)<M$ satisfying $F^{-1}(t_1)<b/a<F^{-1}(t_2)$. For $t_1<t_2$ and $t_3<t_4$ in an interval $(0,T)$ on which $F$ is continuous, the slope-distribution conjecture asserts

$$\lim_{M\rightarrow\infty}\frac{C_f(t_1,t_2,M)}{C_f(t_3,t_4,M)}=\frac{F(t_2)-F(t_1)}{F(t_4)-F(t_3)}.$$

This gives the precise interval-ratio form of the general slope distribution and is supported by the paper's computations for several polynomial degrees.