Period bound conjecture for quadratic rational maps with a rational critical 3-cycle

Let $\phi$ be a quadratic rational function defined over $\mathbb{Q}$, and let a critical $3$-cycle be the set of iterates of a periodic critical point of period $3$. Period bound conjecture for a rational critical 3-cycle. The map $\phi$ has no $\mathbb{Q}$-rational periodic points of period greater than $2$ lying outside the critical cycle. The source proves that periods $3$ and $4$ cannot occur outside the critical cycle, but the asserted exclusion of all greater periods remains open.