Flat-space Dirac factorization ($(i/\partial +m)(i/\partial -m)=-(\square +m^2)$)

The gamma matrix Clifford algebra and commuting partial derivatives give $(/\partial {)}^2=\square$. Thus every free Dirac equation solution also solves the Klein-Gordon equation componentwise. The converse is false without the first-order spinor constraint: the second-order equation alone allows twice as much independent initial data.