  We state a conjectural criterion for identifying global integral points on a
hyperbolic curve over $\mathbb{Z}$ in terms of Selmer schemes inside
non-abelian cohomology functors with coefficients in $\mathbb{Q}_p$-unipotent
fundamental groups. For $\mathbb{P}^1\setminus \{0,1,\infty\}$ and the
complement of the origin in semi-stable elliptic curves of rank 0, we compute
the local image of global Selmer schemes, which then allows us to numerically
confirm our conjecture in a wide range of cases.
