Reversibility of whole-plane SLE for $\kappa >8$

Whole-plane SLE${}_{\kappa }$ is a random fractal curve between two points on the Riemann sphere. Zhan established for $\kappa \le 4$ that whole-plane SLE${}_{\kappa }$ is reversible, meaning invariant in law under conformal automorphisms swapping its endpoints. Miller and Sheffield extended this to $\kappa \le 8$. We prove whole-plane SLE${}_{\kappa }$ is reversible for $\kappa >8$, resolving the final case and answering a conjecture of Viklund and Wang. Our argument depends on a novel mating-of-trees theorem of independent interest, where Liouville quantum gravity on the disk is decorated by an independent radial space-filling SLE curve.