Boundary Theory: An Effective Framework for Gravity from Horizon Thermodynamics

We develop an effective field theory in which gravitational dynamics emerge from the thermodynamic response of boundary degrees of freedom. The framework is organized around the Dirichlet-to-Neumann operator, a well-defined mathematical object that encodes how boundaries respond to bulk perturbations. Starting from established results in horizon thermodynamics (the Unruh effect, the Gibbons-Hawking temperature, and Bekenstein-Hawking entropy bounds), we derive the scaling of the MOND acceleration a₀ ∝ cH₀ from the condition that local acceleration-induced thermodynamics matches cosmic horizon thermodynamics. The coefficient ξ = √(3/2)/(2π) ≈ 0.195 is estimated via dimensional matching at the cosmic horizon, yielding a₀ ≈ 1.3 × 10⁻¹⁰ m/s², in agreement with observations within ~10%. The framework addresses galactic rotation curves and the radial acceleration relation; relativistic phenomena (lensing) and cluster dynamics are beyond its current scope. Falsifiable predictions include a universal a₀ across all galaxies, a relationship Λ = 3a₀²/(ξ²c⁴) linking the cosmological constant to the acceleration scale, and redshift evolution a₀(z) ∝ H(z).