  A triple vector bundle is a cube of vector bundle structures which commute in
the (strict) categorical sense. A grid in a triple vector bundle is a
collection of sections of each bundle structure with certain linearity
properties. A grid provides two routes around each face of the triple vector
bundle, and six routes from the base manifold to the total manifold, the warps
measure the lack of commutativity of these routes.
  In this paper we first prove that the sum of the warps in a triple vector
bundle is zero. The proof we give is intrinsic and, we believe, clearer than
the proof using decompositions given earlier by one of us. We apply this result
to the triple tangent bundle $T^3M$ of a manifold and deduce (as earlier) the
Jacobi identity.
  We further apply the result to the triple vector bundle $T^2A$ for a vector
bundle $A$ using a connection in $A$ to define a grid in $T^2A$. In this case
the curvature emerges from the warp theorem.
