Relational Information Dynamics: A Parameter-Free Derivation of the Galactic Acceleration Floor from de Sitter Modular Theory

We derive the observed galactic acceleration floor g† = 1. 193 × 10⁻¹⁰ m/s² from the synchronisation cost of quantum correlations across the de Sitter cosmological horizon. The central result g† = 2cH₀, dS/π², where H₀, dS = H₀√Ω_Λ, contains no free parameters: the factor 2 is fixed by the Schmidt decomposition theorem and the factor 1/π² by the Basel normalisation of the Margolus-Levitin bound. Validated against 169 SPARC radial acceleration data points with zero free parameters, the prediction gives χ²_ν = 1. 40 and sits within 0. 05σ of the published McGaugh+2016 best-fit on the full 2693-point dataset. Three further predictions follow: (1) a constraint curve H₀ = π²a₀/ (2c√Ω_Λ) connecting the MOND acceleration scale to the Hubble constant, with the 8. 6% Planck residual identified as an algebraic identity equal to the Hubble tension itself; (2) a₀ (z) = const if and only if w = −1, constraining dark energy from galactic dynamics alone; (3) no External Field Effect, distinguishable from MOND with Gaia DR4 wide binary kinematics. Known limitations include the absence of a covariant field equation and the Bullet Cluster lensing displacement.