Prime-divisor density conjecture for stable critically infinite quadratic polynomials

Let $f\in\mathbb{Z}[x]$ be a quadratic polynomial. Call $f$ stable if every iterate $f^n$ is irreducible over $\mathbb{Q}$, and call $f$ critically infinite if the forward orbit of its critical point is infinite. For $a_0\in\mathbb{Z}$, let $P(f,a_0)$ be the set of primes dividing some nonzero term of the orbit defined by $a_n=f(a_{n-1})$, and let $D(P(f,a_0))$ denote its natural density. Prime-divisor density conjecture. If $f$ is stable and critically infinite, then

$$D(P(f,a_0))=0$$

for all $a_0\in\mathbb{Z}$. The paper presents this as the expected generic extension of its main density-zero theorem; it is not proved in the stated generality and remains open.