Eventual stability conjecture for reciprocal quadratic parameters

Let $a\in\mathbb{Z}$ with $a\notin\{0,-1\}$. The rational map $\phi(z)=z^2+1/a$ has degree two, and a pair $(\phi,\alpha)$ is eventually stable when the number of irreducible factors in the iterated preimage polynomials of $\alpha$ is bounded independently of the iterate. Reciprocal quadratic eventual stability conjecture. The map $z^2+1/a$ is eventually stable over $\mathbb{Q}$. This is the exceptional reciprocal-integer family singled out after known results for quadratic polynomials; the source describes these cases as remaining unresolved apart from the obvious exceptions.