  Based on the commutativity of scalar vector fields, an algebraic scheme is
developed which leads to a privileged multi-dimensionally consistent
2n+2n-dimensional integrable partial differential equation with the associated
eigenfunction constituting an infinitesimal symmetry. The "universal" character
of this novel equation of vanishing Pfaffian type is demonstrated by retrieving
and generalising to higher dimensions a great variety of well-known integrable
equations such as the dispersionless KP and Hirota equations and various
avatars of the heavenly equation governing self-dual Einstein spaces.
