Chiral SU(6) Geometry as the Origin of Nuclear Forces, Atomic Shell Structure, and Cosmological Acceleration

We show that a closed 6-dimensional chiral manifold—the space of transitions between left-handed neutron and right-handed proton states—provides a unified geometric origin for three fundamental phenomena. First, the strong and weak nuclear forces emerge as distinct deformation classes of the SU(6) isometry group: chirality-preserving rotations (Cartan generators) and chirality-flipping transitions (off-diagonal root vectors). Second, the aufbau sequence of the periodic table (2, 8, 8, 18, 18, 32) follows from a Madelung drift generated by the Berry connection on this manifold, breaking SO(4) symmetry in an ℓ(ℓ + 1)/n3 pattern that reproduces Madelung’s empirical rule. Third, the MOND acceleration scale is the projection of the 30 internal chiral channels plus 3 spatial translation generators at the Hubble horizon, yielding a0 = cH0/√33 ≈ 1.20 × 10−10m/s². The framework contains one calibrated scale (Rint ≈ 14a0 from the sodium quantum defect) and zero fitted dimensionless parameters. The stiffness Ktrans = 2/3, the cosmological coupling ccosmo = 1/√33, and the Berry drift coefficient κ ≈ 0.44 are derived from geometry. We reduce the framework to known physics—QED, the Standard Model gauge structure, and the neutron lifetime—and present seven falsifiable empirical tests using existing public data.