Quantum Horizon Gravity I: Deriving the MOND Acceleration Scale from De Sitter Geometry

We present Quantum Horizon Gravity (QHG, formerly the Modal-Horizon Framework), a late-time modification to gravity in which the MOND acceleration scale a₀ = 1. 2001 × 10⁻¹⁰ m s⁻² is derived from the Gibbons–Hawking temperature of the de Sitter horizon with no free parameters and 0. 003 per cent agreement with the SH0ES-calibrated value H₀ = 73. 24 km s⁻¹ Mpc⁻¹ — resolving a 43-year open problem in galactic dynamics. QHG introduces a single background scalar ΦRₕ = (Rₕ⁽⁰⁾/Rₕ) ^nγc that couples the cosmic event horizon to the Einstein–Hilbert action, adding no new propagating degree of freedom. The Baryonic Tully–Fisher slope v⁴flat ∝ Mbar is an n-independent algebraic theorem of QHG, not a fit. A joint analysis of 175 SPARC rotation curves returns a coupling exponent ngal = 0. 420 ± 0. 108, consistent at 0. 002σ with the parameter-free theoretical prediction nₒbs = 0. 4198 derived in Paper III. The coupling is dormant during matter and radiation domination by construction from the Bunch–Davies vacuum condition, leaving the CMB, BAO, and BBN unmodified. All Solar System constraints are satisfied with margins of 10⁹–10¹³. A Pantheon+SH0ES cosmological fit (1624 SNe, full systematic covariance) gives ΔAIC = +3. 64 relative to ΛCDM: QHG is cosmologically consistent but does not resolve the Hubble tension. This paper is the first in a series that builds toward a deeper result. The measurement ngal = 0. 420 is the empirical foundation of a completed theoretical programme. In 1995, Jacobson showed that the Einstein field equations follow from the thermodynamics of causal horizons, but left open which horizon dominates galactic dynamics and what its mode spectrum is. QHG answers both questions: the coupling exponent nₒbs = 0. 4198 is a quantum number of the de Sitter vacuum, determined by the representation theory of SO (1, 4) at the cosmic event horizon in precise structural analogy with atomic quantum numbers determined by SO (4) at the nucleus. The galactic measurement ngal = 0. 420 reported here is the observational confirmation of that quantum number. Two independent discriminators from MOND are confirmed in existing SPARC data: declining rotation curves beyond the characteristic radius (Wilcoxon p = 1. 2 × 10⁻¹⁴), and morphology-dependent n at 4. 5σ parametric significance (1. 8σ non-parametric). A previously reported BTFR normalisation gradient does not survive partial-rank control for baryonic mass and is retracted.