A Parameter-Free Derivation of the MOND Acceleration Scale a₀ from the Root System of the Exceptional Lie Group G₂

Milgrom's Modified Newtonian Dynamics (MOND) introduces a critical acceleration scale a₀ ≈ 1.2×10⁻¹⁰ m/s² below which galactic rotation curves depart from Newtonian predictions. The value has stood as a phenomenological input for over four decades, fitted to observation rather than derived from an independent theoretical structure. We present a derivation of a₀ from the root system of the exceptional Lie group G₂, using its first and second Casimir invariants, with no free parameters and no fit to the SPARC dataset performed prior to deriving the constant. The resulting value, a₀ = c·H₀·W₀·(84/89sqrt(12)) ≈ 9.472×10⁻¹¹ m/s², where W₀ = e⁻²ᐟ³ is a structural set-point constant appearing independently elsewhere in this framework, reproduces the radial acceleration relation on the full SPARC sample (175 late-type galaxies, 3,391 data points; Lelli et al. 2016) with RMS = 0.1980 dex — matching the empirically optimal fit to within 0.13% and outperforming standard MOND (RMS = 0.2017 dex). We report the derivation, the empirical test, and the limitations of the comparison.