We develop an effective field theory in which gravitational phenomenology emerges from the thermodynamic response of boundary degrees of freedom on cosmic horizons. The mathematical backbone is the Dirichlet-to-Neumann (DtN) operator, which encodes boundary response; the physical input is that boundaries carry finite information capacity bounded by the Bekenstein-Hawking entropy. The capacity sector is the central result. The boundary carries binary cells whose irreversible activation under gravitational drive obeys Poisson statistics. The resulting congestion barrier, upon optimization, yields the MOND interpolation function μ(x) = x/(1+x) with no free functional choices. The acceleration scale a₀ = ξcH₀ with ξ ≈ 0.195 follows from matching Unruh thermodynamics to the Gibbons-Hawking temperature of the cosmic horizon, giving a₀ ≈ 1.3 × 10⁻¹⁰ m/s² and explaining the cosmic coincidence a₀ ~ cH₀. The microphysical architecture identifies three boundary sectors with a clean division of labor: a rotor/phase sector producing the linear (Newtonian) response, a capacity sector producing the nonlinear (MOND) interpolation, and an amplitude sector supporting the condensate. The Sak criterion confirms that the DtN coupling places the rotor sector in the mean-field universality class, eliminating anomalous BKT exponents. A cluster extension introduces a coexisting cold sector χ providing cluster-scale mass through the tensor sector (standard GR), with lensing following GR sourced by total stress-energy. The framework makes six falsifiable predictions, including a₀(z) ∝ H(z), a Λ–a₀ relation, and the specific derived form of μ(x). An explicit assumption ledger distinguishes established physics, postulates, derived results, and modeling choices throughout.