= Off-shell component count of minimal supergravity
{title2=$6\text{ bosonic}+12\text{ fermionic components}$}
A four-dimensional <Majorana spinor> <gravitino> has $4\times4=16$ real components, minus four local <supersymmetry> gauge functions, leaving twelve before using any <Euler-Lagrange field equation>. A <vierbein> has sixteen real components, minus six local <Lorentz transformation> and four <diffeomorphism> gauge functions, leaving six. Equivalently, a symmetric <metric tensor> has $10-4=6$. The propagating <graviton> and massless <gravitino> each have two states <on shell>. Six bosonic <auxiliary field> components complete an off-shell <supergravity multiplet>.
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