Eventual stability conjecture for reducible cubic polynomials

Let $f(z)=z^3+\frac{1}{c}$ with $c\in\mathbb{Z}\setminus\{0\}$. Here $f^n$ denotes the $n$-fold iterate of $f$. Eventual stability conjecture. If $f(z)$ is reducible over $\mathbb{Q}$, then $f^n(z)$ has exactly two irreducible factors over $\mathbb{Q}$ for each $n\in\mathbb{N}$ and for all $c$. The paper proves this for $|c|\leq 10^{12}$ and conjectures that the result holds for every nonzero integer $c$.