  A non-negative expression, built from the norm of the 3-surface twistor
operator and the energy-momentum tensor of the matter fields on a spacelike
hypersurface, is found which, in the asymptotically flat/hyperboloidal case,
provides a lower bound for the ADM/Bondi--Sachs mass, while on closed
hypersurfaces it gives the first eigenvalue of the Sen--Witten operator. Also
in the closed case, its vanishing is equivalent to the existence of non-trivial
solutions of Witten's gauge condition. Moreover, it is vanishing if and only if
the closed data set is in a flat spacetime with toroidal spatial topology. Thus
it provides a positive definite measure of the strength of the gravitational
field (with physical dimension mass) on closed hypersurfaces, i.e. some sort of
the total mass of closed universes.
