Ji–Xie conjecture on non-conjugate rational maps with equal multiplier spectra

Let $f$ and $g$ be non-conjugate rational maps of degree $d\geq2$. Their multiplier spectrum is the collection of multipliers of periodic points, counted with the multiplicities specified in the spectrum. Two rational maps are equivalent, written $f\sim g$, if they are connected by a finite chain of elementary transformations, where an elementary transformation replaces $h_1\circ h_2$ by $h_2\circ h_1$.

Ji–Xie conjecture. If $f$ and $g$ have the same multiplier spectrum, then one of the following holds: $f$ and $g$ are Lattès maps, or $f\sim g$.

This conjecture identifies Lattès maps and equivalence by elementary transformations as the only known obstructions to injectivity of the multiplier-spectrum map on rational maps. It was posed by Pakovich and conjectured by Ji and Xie; the supplied source gives no resolution, so its status is open.