Null energy condition for a canonical scalar field ($T_{ab}{\ell }^a{\ell }^b=({\ell }^a{\partial }_a\varphi {)}^2\ge 0$)

The classical stress-energy tensor of a canonical scalar field has a gradient-product term and a metric-proportional term. Contracting with a real null vector removes the latter, leaving the displayed square for a real field. This proves the null energy condition for a minimally coupled canonical scalar, including the massless case. It is not a statement about arbitrary curvature couplings, wrong-sign kinetic terms or a renormalized quantum stress-energy tensor.