A Finite Local Quantum Causal Cell with an Einstein-Cartan Infrared Limit

We construct and audit a finite, local, unitary causal-cell model whose reduced long-wavelength sector is Einstein--Cartan gravity coupled to a gapped occupied fermionic environment. The cell combines four tetrahedral body-centered-cubic spatial ports and one temporal normal. Four closed port vectors determine a six-component centered Gram coframe modulo local rotations; the associated torsion-free metric-compatible Cartan connection is unique, and ten centered Lorentz plaquettes reconstruct the complete local Riemann and Einstein tensors. Exact finite covariance is not site valued: the normal--normal bracket produces an oriented edge cochain and repeated brackets close on a path-filtered symplectic algebra. Gapped matter admits an exact number-conserving quantum representation of the same path current, with the recurrence gap canceling from the deformation law. The geometric phase is intrinsic Einstein--Cartan/ADM, whereas a relative-cofactor Port--Julia closed-time-path influence supplies occupied source, retarded response, threshold dissipation, and positive noise. After quotienting three event-section directions and imposing one scalar-capacity constraint, the physical tensor sector has exactly two helicities. On every constant positive coframe the horizontal influence has a common matter--tensor cone and equal helicity kernels. The full finite-band retarded kernel is a scalar Stieltjes rational function: there is one massless pole below the first pair threshold, no tachyon, no negative-residue pole, and positive rank-two threshold noise. Its low-energy expansion contains one helicity-common quartic correction and sixth-order pole remainders. Nonlinear Bianchi-I, Gowdy, and weak-curvature audits reproduce the DeWitt kinetic form, constraint propagation, and Gauss--Codazzi curvature. The construction does not derive the global capacity sector, the cosmological constant, Standard-Model parameters, or the dimensionful Newton scale; these are stated explicitly as external or boundary data. The result is a constructive finite-cell universality theorem, not a claim that gravity is the phase of a single occupied determinant.