Volume M: OP-2 of NEA — The Manifest Manifold: Complete Derivation of the Einstein Field Equations from C8 Causal Graph Dynamics

The derivation of the Einstein field equations from the discrete C8 causal graph dynamics of the N.E.A. (Network Emergent Architecture) framework. The proof proceeds in four sequential modules. OP-2a proves the C^2 convergence of the discrete Green's function to 1/(4πr) via singularity subtraction. OP-2b proves the convergence of direction-averaged Ollivier-Ricci curvature to the Ricci scalar. OP-2c proves the unique reconstruction of the full Ricci tensor via an explicit 6×6 invertible linear system. OP-2d completes the programme by identifying the Einstein tensor with the stress-energy tensor of stitching deficits. Together, these results provide a self-contained proof that classical gravity emerges as the rigorous coarse-grained limit of a finite-bandwidth causal graph governed solely by global enthalpy conservation, the principle of least action, and the node bandwidth constraint B=1.