The preceding paper in this sequence connected matter-first spin networks to the simplicity-constrained EPRL vertex: matter-line frames generate spacetime-algebra bivectors, the EPRLmap selects a ray in the bivector invariant plane, and the Lorentzian four-simplex amplitude can be evaluated as a nite-cuto tensor network on K5. That result was kinematical and vertex-local. This paper asks the next question: when curvature is present, can the matter determinant see it, and can it back-react on the spin-foam flatness tendency? We build a finite hinge-link model in which several four-simplices meet around an internal triangle. The Regge decit ϵh = 2π −Pσ⊃h Θσh is represented as a rotation in the two-plane normal to the hinge,with spin lift Uspin(ϵh). The first exact result is the holonomy obstruction det(I − Uspin) = 16 sin^4(ϵh/4), which vanishes in the flat sector, modulo the expected spinorial 4π periodicity. A finite graph Dirac operator on the hinge link reproduces the same obstruction and develops a curvature-induced spectral gap. Integrating out fermions therefore suppresses the near-at zero-modesector in a one-hinge toy model, opposing the gravitational atness preference. For two hinges,disconnected link graphs factorise exactly, whereas edge-sharing link graphs have a non-zero determinant interaction; matter propagation then induces a curvature-curvature correlation between neighbouring defects. Finally we add a chiral Spin(4) = SU(2)+ × SU(2)− split. A single finite hinge determinant is phase-trivial, arg det(Dχ + m) = 0, so it can bias chiral variances but cannot by itself generate orientation-sign flow. The parity-odd channel in four dimensions is instead the Pontryagin pairing tr(γ5Σ1Σ2) ∼ B1 ∧ B2, non-zero only for transverse hinge planes. The result is not a continuum limit or a derivation of the full spin-foam measure. It is a controlled finite-complex mechanism: fermion determinants are holonomy-sensitive functionals of Regge decits and can induce matter-mediated curvature correlations on spin-foam hinge links.