Deriving the Cosmological Constant from the Global Entropic Consistency Principle

We propose that the cosmological constant arises as an emergent energy scale from the Global Entropic Consistency Principle (GEC), which enforces delayed compensation of local entropy perturbations across the cosmological event horizon. Finite signal propagation at speed c introduces a single macroscopic timescale τ = R_e / c. We show that the deterministic dynamics of the associated global residual mode yield an effective energy density ρ_Λ^GEC proportional to τ⁻² ∼ R_e⁻², while stochastic fluctuations governed by an Ornstein–Uhlenbeck process are parametrically suppressed as ρ_stoch ∼ R_e⁻³. When the compensating boundary is identified with the cosmological event horizon, the resulting Friedmann dynamics reproduce the observed expansion history: a matter-dominated early phase, transition to acceleration at z ≈ 0.6, and a late-time de Sitter phase. The present-day value satisfies ρ_Λ^GEC ∼ 10⁻¹²² (in Planck units), determined directly from the observed event-horizon size R_e ∼ 10⁶¹ without fine-tuning. A microscopic realization is provided on a toroidal qutrit lattice in the UTHC phase.