To every trivalent tropical curve in an n-dimensional affine manifold with metric, we'll build a n-dimensional manifold with a locally CAT(0) metric. We'll then switch gears and talk about a relationship between coherent sheaves on projective space and modules over the free group. At the end we'll tie both stories together, giving us an algebraic geometric interpretation of a Weinstein-neighborhood of a tropical Lagrangian via the mirror to Viterbo restriction.