© Springer-Verlag Berlin Heidelberg 2012. We study which rational points of the Jacobian of ℙ1-{0,1,∞} can be lifted to sections of geometrically 3-nilpotent quotients of étale π1 over the absolute Galois group. This is equivalent to evaluating certain triple Massey products of elements of k* ⊆ H1(Gk, ℤ(1)) or H1(Gk,ℤ/2ℤ). For k = ℚp or R, we give a complete mod 2 calculation. This permits some mod 2 calculations for k = ℚ. These are computations of obstructions of Jordan Ellenberg.