A Block-Normalised de Sitter Boundary-Harmonic Derivation of the Galactic Acceleration Threshold and a Closed-Form Radial Acceleration Relation

The radial acceleration relation (RAR) of disc galaxies is governed by a single acceleration scale, a₀ ≈ 1.20×10⁻¹⁰ m s⁻², whose origin has long been an open question. We report a two-input closed-form relation for this scale and a corresponding closed-form RAR law. From the two late-time cosmological parameters (H₀, Ω_Λ) alone we obtain a₀ = c H₀ / (2π Ω_Λ^{3/8}) = 1.20055×10⁻¹⁰ m s⁻² at Planck-2018 central values, with no galaxy-level fit parameter; the bare Hubble-temperature scale c H₀/(2π) undershoots the empirical value by about 13%, and the Ω_Λ^{−3/8} factor supplies the missing normalisation. Built on this scale, the closed-form law g_obs² = g_bar² + a₀ g_bar · (1 + √(3/2)·√(g_bar/a₀)) · exp[ −e g_bar / (2π Ω_Λ^{3/8} a₀) ] has the correct deep-MOND and Newtonian limits and, with no parameter fitted to galaxy kinematics, matches the SPARC RAR at a level comparable to the standard empirical interpolation under the same fixed baryonic model. On the full SPARC Q=1 sample (93 galaxies, N=2060 radial points, no outlier rejection) it is comparable to the McGaugh interpolation (χ²/N = 44.84 versus 45.48 under a common relative-scoring prescription, the difference interpreted descriptively rather than as a calibrated likelihood significance), while a one-parameter free-a₀ fit returns a₀(free) = 1.1999×10⁻¹⁰ m s⁻², in 0.05% agreement with the cosmological prediction. We present these as empirical, falsifiable closed-form relations; the microscopic mechanism behind the Ω_Λ^{−3/8}, √(3/2), and e factors is developed in a companion manuscript.