Two Planck constants from brane localisation: gravitational and electromagnetic quantum scales on a Kähler compactification

In string compactifications on Kähler manifolds, the Gromov non-squeezing theorem applies separately to geometrically distinct sub-manifolds. Standard Model fields localised on a non-perturbatively stabilised small cycle have their quantum scale set by ℏ_EM = c_Gr(D_s), which is constant. Gravitational degrees of freedom propagating through the full compact space have their quantum scale set by ℏ_grav = c_Gr(K), which varies with the compact volume as μ^{1/3}. This produces two distinct Planck constants that coincide in strong-field environments (μ = 1) but diverge in the MOND regime (μ < 1). Five observational tests are presented: Big Bang nucleosynthesis, CMB at recombination, quasar absorption spectra, pulsar timing (Ġ/G), and the Chandrasekhar mass in ultra-diffuse galaxies. All five are satisfied. The nearest-term falsification target is SKA pulsar timing at projected sensitivity ~10⁻¹³ yr⁻¹ by 2035.