Forcing the ${\mathrm{\Pi }}_n^1$-Uniformization Property

We generically construct a model in which the ${\mathrm{\Pi }}_3^1$-uniformization property is true, thus lowering the best known consistency strength from the existence of $M_1^{\mathrm{\#}}$ to just $\mathsf{Z}\mathsf{F}\mathsf{C}$. The forcing construction can be adapted to work over canonical inner models with Woodin cardinals, which yields, for the first time, universes where the ${\mathrm{\Pi }}_{2n}^1$-uniformization property holds for $n>1$, thus producing models which contradict the natural $\mathsf{P}\mathsf{D}$-induced pattern.