Thomas–Williams' rowmotion order conjecture for rational Tamari lattices

Let $a$ and $b$ be relatively prime positive integers. Let $\operatorname{Tam}(a,b)$ be the rational Tamari lattice of lattice paths from $(0,0)$ to $(a,b)$ lying strictly above $y=(b/a)x$ except at their endpoints, and let $\operatorname{Row}$ denote its rowmotion operator.

Thomas–Williams' conjecture. The operator

$$\operatorname{Row}\colon\operatorname{Tam}(a,b)\to\operatorname{Tam}(a,b)$$

has order $a+b-1$.

This conjecture gives the period of rowmotion on every rational Tamari lattice. The paper proves it for the subfamily of $m$-Tamari lattices, while the general case remains open.