  We prove the conjecture made by Bern, Dixon, Dunbar, and Kosower that
describes a simple dimension shifting relationship between the one-loop
structure of N = 4 MHV amplitudes and all-plus helicity amplitudes in pure
Yang-Mills theory. The proof captures all orders in dimensional regularisation
using unitarity cuts, by combining massive spinor-helicity with Coulomb-branch
supersymmetry. The form of these amplitudes can be given in terms of pentagon
and box integrals using a generalised D-dimensional unitarity technique which
captures the full amplitude to all multiplicities.
