Event-State Theory VI: General Relativity as the Infrared Effective Theory of Discrete Causal Optimization

Abstract We present a constrained derivation sketch showing how the Einstein field equations arise as the infrared effective description of a discrete successor-state selection principle. Event-State Theory (EST) posits that the universe evolves through a sequence of discrete global states $\{\Psi_n\}$, where admissible successor states are selected by minimizing (or probabilistically weighting) a computational cost functional $J(\Psi_n\to\Psi_{n+1})$. Focusing on the geometric contribution $J_{\mathrm{geom}}$—the cost associated with the causal/update structure itself—we argue that systematic anisotropies in local update neighborhoods constitute an intrinsic ``lattice tax''. Under coarse-graining, the macroscopic response to reducing this tax is encoded by an emergent metric field. Assuming locality, emergent diffeomorphism invariance, and a second-order infrared truncation, the leading continuum action is constrained to the Einstein--Hilbert form (plus a cosmological constant and higher-derivative corrections). The Einstein equations follow by variation. We explicitly distinguish (I) assumptions required for the infrared effective field theory step from (II) open problems needed for a full microscopic-to-continuum coefficient match.