Spacetime torsion fixes the mass and spin of gravitationally produced dark matter

The gravitational production of dark matter from stochastic gravitational waves requires the produced fermion to acquire a mass by unspecified late-time physics. We show that this mass is supplied by spacetime torsion alone – no Higgs sector and no free mass parameter. In the Quadratic Spinor Lagrangian formulation of general relativity, extended to Einstein–Cartan, a cosmological spinor condensate generates a vectorial trace torsion $K\propto \dot{\chi }\mathrm{/}\chi$; an explicit Clifford reduction confers on the produced spin-1/2 fermion a pure Dirac mass $M_{\mathrm{e}\mathrm{f}\mathrm{f}}=(1\mathrm{/}\sqrt{6})\mathrm{\mid }\dot{\chi }\mathrm{/}\chi \mathrm{\mid }$, with no pseudoscalar or cross terms, locked to the Hubble rate at production, $M_{\mathrm{e}\mathrm{f}\mathrm{f}}\simeq (c_{\chi }\mathrm{/}\sqrt{6})H_{\ast }$. The relic abundance is then a one-parameter prediction, $\mathrm{\Omega }{h}^2\propto H_{\ast }^{5\mathrm{/}2}$, and the spin is fixed: the same framework admits no propagating spin-3/2 mode, so the composite spin-1/2 Dirac fermion is its unique dark-matter candidate.