Derivation of the MOND acceleration scale a₀ = cH₀/(2π) from a cosmological-horizon constraint on inertial response

We derive the Milgrom MOND acceleration scale a₀ from a cosmological-horizon constraint on inertial response in a substrate-field framework. The argument requires only that inertia is mediated by substrate excitations propagating at the speed of light c and is bounded in spatial reach by the cosmological horizon distance c/H₀. The de Sitter horizon temperature T_dS = ℏH₀/(2πk_B) defines, via the Unruh-Davies relation a = 2πk_BTc/ℏ, a corresponding acceleration scale

                  a₀ = cH₀/(2π) ≈ 1.05 × 10⁻¹⁰ m s⁻²

below which inertial response cannot fully form within the horizon-bounded spacetime region available. This matches the empirically-determined Milgrom MOND scale a₀^obs ≈ 1.2 × 10⁻¹⁰ m s⁻² to approximately 13%, with no free parameters fitted to observation. We discuss the implications for galaxy rotation curves, the radial acceleration relation, the Tully-Fisher relation, and the wide-binary test, and we examine the prediction's sensitivity to the value of H₀ and to its variation across cosmic time. The result provides a parameter-free, falsifiable derivation of the MOND scale that does not require dark matter and that situates the modified-inertia phenomenology in a specific microphysical setting.