Discrete Entropic Gravity on a Cubic Graph: Emergent Newton and MOND Regimes with Λ-Locked Screening

We construct a discrete gravity operator defined on a cubic graph with entropic flux weighting between nodes. The operator reproduces (i) Newtonian 1/r² scaling in the strong-field regime, (ii) MOND-like 1/r scaling in the low-acceleration regime, (iii) a transition scale set by a bulk entropic reservoir proportional to Λ, (iv) broken superposition, and (v) an external field effect (EFE). No continuum metric or General Relativity equations are assumed. The theory is defined purely on graph topology. Systematic convergence and kill-tests are performed. A non-trivial prefactor C ≈ 2.32 emerges independent of spherical vs cubic binning, indicating a discrete renormalization of the infrared response. This implies an effective acceleration scale a₀,eff = C² a₀ ≈ 5.4 a₀, which deviates from the standard MOND value and must be accounted for in any phenomenological comparison. A minimal cosmological stability check confirms σ₈ = 0.805 (vs ΛCDM 0.811) with growth suppression ε₀ = 0.8%, verifying the operator does not produce runaway structure growth. The perturbation-level μ(a) < 1 channel remains disabled in this test.