N=8 Supergravity from Positivity.

The duality between color and kinematics brings many simplifications to the construction of scattering amplitudes. Here, we show that satisfaction of the tree-level Bern-Carrasco-Johansson relations can dramatically simplify loop computations even when the loop-level relations are not explicitly satisfied. We introduce an agglomerative algorithm, color-dual cut tiling, that builds the entire integrand from the simplest on-shell conditions applied to a seed of off-shell integrand information.