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We show that the Vojta (or Hall-Lang) conjecture implies that the arborealGalois representations in a 1-parameter family of quadratic polynomials aresurjective if and only if they surject onto some finite and uniform quotient.As an application, we use the Vojta conjecture, our uniformity theorem over$\mathbb{Q}(t)$, and Hilbert's irreducibility theorem to prove that the primedivisors of many quadratic orbits have density zero.

The Vojta conjecture implies Galois rigidity in dynamical families