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 κSD > 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 dₛ = 4 is independently certified (: \graph\ₛpectral\dim\ₜhermodynamic\ₗimit; numerical dₛ = 4. 153 ± 0. 05, the expected finite-size correction). A discrete Einstein-equation regression yields κ_ excess = 4. 84T₀0^ (CA) (R² = 0. 20, p = 1. 37×10^-148). SR time dilation emerges from AFCA inner first-passage time τc 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.
Nova Spivack (Tue,) studied this question.