On reductions of Selmer sections

We consider reductions of Selmer sections of the étale homotopy sequence of a hyperbolic curve over a number field. We show that the conjugacy class of a noncuspidal Selmer section is uniquely determined by its reduction on a set of density one. Moreover, we show that a noncuspidal Selmer section reduces to cusps only on a set of density zero, at least after a finite field extension.