  We devise a new technique to prove two-dimensional crystallization results in
the square lattice for finite particle systems. We apply this strategy to
energy minimizers of configurational energies featuring two-body short-ranged
particle interactions and three-body angular potentials favoring bond-angles of
the square lattice. To each configuration, we associate its bond graph which is
then suitably modified by identifying chains of successive atoms. This method,
called stratification, reduces the crystallization problem to a simple
minimization that corresponds to a proof via slicing of the isoperimetric
inequality in $\ell^1$. As a byproduct, we also prove a fluctuation estimate
for minimizers of the configurational energy, known as the $n^{3/4}$-law.
