Emergent Gravity from Rule 110 Cellular Automaton

Starting from the Rule~110 CA within the GTE framework, we show that the deviation-based Ollivier–Ricci curvature of the causal graph satisfies the discrete vacuum Einstein equation G_μν = 0 ( , zero sorry) and exhibits κ_SD > 0 consistent with G_μν = 8π T_μν ( ). A formal correspondence between MDL minimality and the Lovelock uniqueness theorem ( ) establishes Einsteinian gravity as the unique diffeomorphism-invariant effective theory compatible with the GTE substrate. Spacetime dimension D = 4 is machine-certified ( : \_spacetime\_dimension, \_dim\_fmdl\_structure\_forced, zero sorry); the causal-graph spectral dimension d_s = 4 is independently certified ( : \_graph\_spectral\_dim\_thermodynamic\_limit; numerical d_s = 4.153 ± 0.05, the expected finite-size correction). A discrete Einstein-equation regression yields κ_ excess = 4.84T_00^( CA) (R^2 = 0.20, p = 1.37×10^-148). SR time dilation emerges from AFCA inner first-passage time τ_c to 8.7\% best-pair accuracy; the CMCA inner-clock construction (P41) achieves 5.79\% error (the M=7 Nyquist floor). Color confinement and an unconditional QFT mass gap follow from the PSC-admissible kink sector ( , zero sorry, zero axioms). Newtonian gravity from cross-tape PMDL minimization is established in the three-tape companion~ ( ). The primary open problem is the smooth continuum limit (a → 0 recovering continuous SO(1,3)), as in lattice QCD.