= Solution
The first-order fermionic kinetic term produces second-class <momentum> <constraints>. After eliminating them, the canonical <graded Dirac brackets> are
$$
\boxed{\{x^m,p_n\}_D=\delta^m{}_n,\qquad\{\psi^m,\psi^n\}_D=-i\eta^{mn},}
$$
with other mixed brackets zero. The bracket of two odd variables is symmetric, consistently with the <graded Poisson bracket>. The <constraint algebra> is
$$
\boxed{\{\mathcal Q,\mathcal Q\}_D=-ip^2=-2i\mathcal H,\qquad\{\mathcal Q,\mathcal H\}_D=0,\qquad\{\mathcal H,\mathcal H\}_D=0.}
$$
It is the <worldline supersymmetry algebra>: the square of the fermionic <constraint> generates the <Hamiltonian> <constraint>.
With $\hbar=1$, quantization converts these to
$$
[\widehat x^m,\widehat p_n]=i\delta^m{}_n,\qquad\{\widehat\psi^m,\widehat\psi^n\}_+=\eta^{mn}.
$$
Represent the fermions by <Gamma matrices>, $\widehat\psi^m=\gamma^m/\sqrt2$, where $\{\gamma^m,\gamma^n\}_+=2\eta^{mn}$, and $\widehat p_m=-i\partial_m$. The wavefunction is a <Dirac spinor>. Its physical-state <constraint> is
$$
\boxed{\widehat{\mathcal Q}\Psi=-\frac{i}{\sqrt2}\gamma^m\partial_m\Psi=0,}
$$
which is exactly the <massless Dirac equation>. Moreover $\widehat{\mathcal Q}^{\,2}=\widehat{\mathcal H}=-\square_D/2$, so this equation implies the remaining mass-shell <constraint>. Conversely, a solution of the <massless Dirac equation> satisfies both <constraints>. The Klein-Gordon <constraint> alone would not impose the spinorial first-order equation.
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