We extend the Einstein-Hilbert action by two terms-an R² elastic correction (Starobinsky) and a vacuum-matter coupling (1 + 2α)-where the coupling α is derived from QCD sigma terms. Taking the trace of the resulting field equations and imposing a self-consistency condition on the vacuum-matter-metric cycle, with the non-perturbative curvature response estimated via naive dimensional analysis (NDA), yields a closed-form expression for the cosmological constant: Λ0 = α · fb · σ⁶ / mPl⁴. Every input is measured independently. Using the derived α = 0.005, the result is Λ0 ≈ 3.0 × 10−52 m−2, compared to the observed 1.1 × 10−52 m−2 (ratio 2.8). The nonlinear screening factor entering α is confirmed by particle-mesh N-body simulations at 128³ resolution presented here, which yield a converged screening of 3.9× via Richardson extrapolation. Five falsifiable predictions are stated. The simulation code is provided in Appendix A. Abstract We extend the Einstein-Hilbert action by two terms-an R² elastic correction (Starobinsky) and a vacuum-matter coupling (1 + 2α)-where the coupling α is derived from QCD sigma terms. Taking the trace of the resulting field equations and imposing a self-consistency condition on the vacuum-matter-metric cycle, with the non-perturbative curvature response estimated via naive dimensional analysis (NDA), yields a closed-form expression for the cosmological constant: Λ0 = α · fb · σ⁶ / mPl⁴. Every input is measured independently. Using the derived α = 0.005, the result is Λ0 ≈ 3.0 × 10 −52 m −2 , compared to the observed 1.1 × 10 −52 m −2 (ratio 2.8). The nonlinear screening factor entering α is confirmed by particle-mesh N-body simulations at 128³ resolution presented here, which yield a converged screening of 3.9× via Richardson extrapolation. Five falsifiable predictions are stated. The simulation code is provided in Appendix A.