  Energy conditions are crucial for understanding why exotic phenomena such as
traversable wormholes and closed timelike curves remain elusive. In this paper,
we prove the Double Smeared Null Energy Condition (DSNEC) for the fermionic
free theory in 4-dimensional flat Minkowski space-time, extending previous work
on the same energy condition for the bosonic case [1][2] by adapting Fewster
and Mistry's method [3] to the energy-momentum tensor $T_{++}$. A notable
difference from previous works lies in the presence of the $\gamma_0 \gamma_+$
matrix in $T_{++}$, causing a loss of symmetry. This challenge is addressed by
making use of its square-root matrix. We provide explicit analytic results for
the massless case as well as numerical insights for the mass-dependence of the
bound in the case of Gaussian smearing.
