Cosmological Growth Constraints on Λ-Locked Discrete Entropic Gravity

We test the cosmological viability of a discrete entropic gravity operator exhibiting Newtonian and MOND-like regimes with Λ-locked infrared screening. The effective gravitational coupling G_eff(k,a) derived from the discrete operator is embedded into the linear growth equation for matter perturbations. We compare three scenarios: (i) Λ-locked transition at super-Hubble scale, (ii) transition at 10 Mpc, and (iii) transition at 1 Mpc. We show that only Λ-locking preserves realistic structure growth (σ₈ ≈ 0.8). Any sub-Hubble transition scale leads to catastrophic overgrowth (σ₈ >> 1), establishing Λ-locking as a necessary condition for cosmological consistency.