Loop quantum gravity (LQG) is usually formulated as a quantisation of geometry, while operational measurements of length, time, and orientation are made through relations among matter fields. Penrose’s combinatorial spacetime and Altaisky’s recent locally Lorentzian matter-spin-network construction suggest a matter-first route: interaction events form the vertices of a graph, fermion-line segments form its edges, and geometry is reconstructed from the relations carried by those lines. We develop this kinematical proposal into an induced dynamical model with a computable discrete field equation. In the spacetime algebra Cl(1, 3), the SL(2, C) interaction vertices become versors; their sandwich action transports the matter-built tetrad, agrees with both the Hermitian-matrix and Ruehl Lorentz maps, and sends elementary areas to simple grade-two blades. Loop curvature is the bivector logarithm of a holonomy and is classified by the scalar and pseudoscalar invariants of B2; the generic loxodromic case is handled by a closed-form commuting elliptic—hyperbolic split. Because the discrete Grassmann matter action is bilinear, its path integral is the exact fermion determinant Z = det D. On an oriented graph Dirac operator, gauge invariance reduces Z to a functional of cycle-space holonomies, whileloops that share interaction events fail to factorise. The connected non-factorising determinant defines the interaction part of the effective action. Varying Seff = − log | det D| gives a local, gauge-covariant stationarity condition relating each independent cycle connection to the fermion propagator. Flat geometry solves the homogeneous equation as a Lorentzian saddle, and fixed boundary holonomies source curvature in the remaining cycles. We demonstrate the construction on the tetrahedral S^2 toy universe and on the K5 four-simplex 1-skeleton. The resulting equation is induced, Sakharov-style, and no continuum limit to Einstein gravity is claimed.